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Computational analysis of schizophrenia: Implementation of a multivariate model of anatomical differences

Computational analysis of schizophrenia:
Implementation of a multivariate model of
anatomical differences
Gemma C. Monté Rubio
Aquesta tesi doctoral està subjecta a la llicència ReconeixementCompartirIgual 4.0. Espanya de Creative Commons.
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Esta tesis doctoral está sujeta a la licencia Reconocimiento - NoComercial – CompartirIgual
4.0. España de Creative Commons.
This doctoral thesis is licensed under the Creative Commons Attribution-NonCommercialShareAlike 4.0. Spain License.
University of Barcelona UB
Faculty of Medicine – Biomedicine Doctorate Program
October 2015
Computational analysis of schizophrenia:
Implementation of a multivariate model of anatomical
differences
Gemma C. Monté Rubio
Supervisors:
Prof. John Ashburner
Dr. Carles Falcón
Dra. Edith Pomarol-Clotet
Wellcome Trust Centre
University of Barcelona,
FIDMAG Research Foundation,
for Neuroimaging, UK.
Spain.
Spain.
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
This thesis was carried out at the FIDMAG Sisters Hospitallers Research Foundation, in
Sant Boi de Llobregat, and written at the IDIBAPS, in Barcelona (Spain).
The FIDMAG Research Foundation provided the data used in the study related to the
Schizophrenia, and financially supported the stage of three months at the FIL methods
group, in the Wellcome Trust Centre for Neuroimaging, London (UK).
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
A la meva mare Mei,
sense tu saps que no ho hagués aconseguit.
I a la meva filla Ariadna,
aquí tens on he invertit el temps que t’he robat.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Agraïments
Aquesta tesi no només consisteix en el que tot seguit està escrit, més enllà del text simbolitza una
part important de la meva vida, i concloure-la es converteix en un acte simbòlic: enllestir un
període per començar-ne un de nou. En l'àmbit científic i professional m’ha enriquit moltíssim, però
en l'àmbit personal també ha fet molt per mi. Per bé, ja no sóc la mateixa que la va començar.
He d’agrair de tot cor el suport que he rebut durant aquests anys a moltes persones. En primer lloc
als meus directors: el Dr. Carles Falcón, que sempre (des que ens vam conèixer, molt abans del
doctorat i davant adversitats) ha estat al costat i molt especialment durant la tesi, fent de guia,
donant suport i sent un amic en el sentit més ple de la paraula. No sé com podré agrair-te tot el que
has fet! Al Prof. John Ashburner, brillant científic i bellíssima persona, qui va apostar per mi de bon
començament amb totes les de la llei, i que ha estat al peu del canó fins al darrer moment. John,
thanks for believing in me, and also for those moments that we shared with your wonderful family,
Hester and little Sophie, we have won a friendship! I la Dra. Edith Pomarol-Clotet, qui sempre ha
estat receptiva, donant ànims i suport més enllà del que era establert. Sense el teu suport i el del Dr.
Salvador Sarró, no hauria fet l’estada a Londres, entre altres coses!
A més de directora, l’Edith ha estat la meva cap durant cinc anys a la FIDMAG, així com el Prof. Peter
Mckenna, qui com ella m'ha aportat molt. I enjoyed our exchange sessions about science and
philosophy. A la FIDMAG he viscut un període molt enriquidor del que he tret moltes coses, el
millor de tot: les persones. He conegut companys de qui he après de neuroimatge i m’he endut
amistats que porto al cor. Eulàlia, Alicia i Sònia, Bàrbara, Jesús, Bene i Ramón, Èlia, Rumi i Ali, Erick,
Rai i Quim, Salva gràcies per recolzar-me, i tenir sempre paraules bones i de suport, Pi, Silvia, Ana i
sobretot la meva Maria sabeu que us estimo molt.
Acabo d’estrenar etapa a l’IDIBAPS per a la Unitat de Demències del Clínic, amb la gent de la
plataforma de Neuroimatge del CEK i de la Fundació Pasqual Maragall. Des del primer moment
m’he sentit acollida per un grup de gent integradora, plena de motivació i inquietuds. Gràcies Oriol,
Isa i a tots per fer-m’ho tan fàcil. Sobretot vull agrair al meu cap, el Dr. José Luis Molinuevo que
m’hagi donat aquest periode per enllestir la tesi. Mil gracias por tu generosidad, tu paciencia y tu
calidad humana. I al Dr. Juan Domingo Gispert, gràcies per facilitar tant aquesta tesi i fer-me costat.
Els inicis treballant amb tu i el teu equip han estat estimulants i prometedors d’una etapa que
començo amb il·lusió.
Fora de l’àmbit professional bons amics m’han donat l’energia, m’han ajudat a buscar la motivació i
no m’han deixat caure, persones increïbles que sempre hi son, que sàpiguen que a mi també em
tenen: En Giuseppe i l’Elisabeth, dues grans persones que ens acullen sempre amb els braços oberts
i ens ho donen tot, sou de la nostra familia! Svetlana, thanks for your warmth and help, our
friendship began with this thesis but will go beyond it. Emma, Isabel, Montse, Roser i Mariam sou
molt especials! Fefa, repartir tareas del día a día contigo ha sido un respiro. Marifí, Angel Luis i a
tots aquells que m’heu encoratjat, gràcies pel vostre suport.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Finalment, com no pot ser de cap altra manera, a la meva família, la meva germana Marina i els
meus pares, de qui em sento tan orgullosa que no hi cap en aquestes línies, les millors persones que
conec, un model a seguir. Gràcies perquè durant tota la meva vida heu estat una font
de recolzament i amor incondicional. També a la Laura, I als meus tiets i cosines, amb qui junts fem
pinya davant l’adversitat. I al meu marit i la meva filla, que em donen tot l’amor i em fan mirar de
ser cada dia millor persona, gràcies per recolzar-me i no retreure’m ni un segon de tot el temps que
us he pres per donar-li a aquesta tesi.
A tots els que m’heu ajudat a arribar a aquest dia: gràcies, perquè per vosaltres és que no he
abandonat.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Abbreviations
AUC
Area Under the Curve
BET
Brain Extraction Tool
BF
Bayes Factor
BG
Background tissue
BMI
Body mass index
CSF
Cerebrospinal fluid
CV/LOO-CV
Cross Validation / Leave-one-out Cross Validation
DARTEL
Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra
FAST
FMRIB's Automated Segmentation Tool
FSL
FMRIB Software Library
FWHM
Full-width at half maximum
GM
Grey matter
GM(+)/(-)
False positives / false negatives
GP
Gaussian Processes
GS
Gold standard
LDDMM
Large Deformation Diffeomorphic Metric Mapping
NS
New Segmentation
RMS
Root Mean Squared
SPM
Statistical Parametric Mapping
SVE
Segmentation Validation Engine
TIV
Total Intracranial Volume
US
Unified Segmentation
VBM
Voxel-Based Morphometry
WM
White matter
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Contents
1.
Introduction _________________________________________________________________________ 13
1.1
1.1.1
2.
Diffeomorphic image registration by Geodesic Shooting_____________________ 24
1.3
Gaussian Process Models __________________________________________________________ 26
1.4
Data feature representation ______________________________________________________ 28
Objectives ____________________________________________________________________________ 29
3.1
Motivation & Objectives ___________________________________________________________ 32
3.2
Material & Methods_________________________________________________________________ 32
3.3
3.3.1
3.3.2
Results ________________________________________________________________________________ 43
Preliminary evaluations _________________________________________________________________ 43
Experimental design _____________________________________________________________________ 49
Motivation & Objectives ___________________________________________________________ 70
4.2
Material & Methods_________________________________________________________________ 71
Dataset ____________________________________________________________________________________ 71
Preprocessing ____________________________________________________________________________ 71
Data for structural feature representation ______________________________________________ 72
4.3
Performance evaluation ___________________________________________________________ 76
4.4
Results ________________________________________________________________________________ 79
GP Regression ____________________________________________________________________________ 79
GP Classification __________________________________________________________________________ 84
Study 3: Application to Schizophrenia __________________________________________ 87
5.1
Motivation & Objectives ___________________________________________________________ 88
5.2
Material & Methods_________________________________________________________________ 88
5.2.1
5.2.2
5.3
5.3.1
5.3.2
Participants_______________________________________________________________________________ 88
MRI preprocessing _______________________________________________________________________ 89
Results ________________________________________________________________________________ 91
VBM _______________________________________________________________________________________ 91
GP classification __________________________________________________________________________ 92
Discussion ___________________________________________________________________________ 95
6.1
7.
8.
32
33
33
36
4.1
4.4.1
4.4.2
6.
Data _______________________________________________________________________________________
Software __________________________________________________________________________________
Preliminary evaluations _________________________________________________________________
Experimental design _____________________________________________________________________
Study 2: Feature selection for structural pattern recognition studies_____ 69
4.2.1
4.2.2
4.2.3
5.
Roadmap _____________________________________________________________________________ 30
Study 1: Influence of segmentation model in VBM-type preprocessing____ 31
3.2.1
3.2.2
3.2.3
3.2.4
4.
Comparative description of the models steps ___________________________________________ 18
1.2
2.1
3.
Algorithms for brain image segmentation ______________________________________ 17
Outlook ______________________________________________________________________________ 101
Conclusions _________________________________________________________________________ 103
References __________________________________________________________________________ 105
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
1. Introduction
Schizophrenia is a chronic mental disease that is characterised by a distorted
interpretation of reality. This disabling brain disorder can be treated, but even though it
helps, most patients have to cope with the symptoms throughout all their lives (Patiny,
Constant, and Symann 2015; de Paula et al. 2015). In such patients, the clinical picture is
often undifferentiated at first presentation, and it is unclear which of them are at most risk
of developing chronic schizophrenia or bipolar disorder. Categorization of mental diseases
remains controversial, because current diagnoses depend on imprecise categorical
distinctions, with arbitrary cutoffs (Thaker 2008). This is a problem for the patient, who
spends longer without appropriate treatment with the consequent decline. It is also a
problem due to the additional costs, both social and economic, arising from patients who
are not correctly treated. Current diagnostics regarding schizophrenia and other mental
diseases are based predominantly on phenomenological criteria and are not supported by
biomarkers. The identification of relevant disease biomarkers and testing them as novel
targets for treatment are of crucial interest for the field (Ivleva et al. 2013).
Chronic schizophrenia has been widely studied, and there are consistent findings that
have allowed the characterization of the anatomical pattern associated with this disease.
The neuroimaging field has contributed to this knowledge. Structural Magnetic Resonance
Imaging (MRI) is a non-invasive imaging modality that allows the study of in vivo
morphological features in healthy and impaired brain anatomy. Many works in the
literature have shown that structural MRI data contribute in research and can aid in
clinical assessment (Feinstein et al. 2004; Frisoni et al. 2010). Several studies have
contributed knowledge about the pattern of damage associated with the disease (Honea et
al. 2005; Bora et al. 2011; Ellison-Wright and Bullmore 2010), and how in these areas
abnormalities of brain function and axonal diffusion have also been found (PomarolClotet, Canales-Rodríguez, et al. 2010; Salgado-Pineda et al. 2011).
Morphologically, schizophrenia is characterized by a reduction, of around 2%, in whole
brain volume. Locally, larger reductions in regions such as the frontal lobe, in about 50%
of VBM studies, and hippocampus, insula, temporal and parietal cortices, in about 20%, are
reported (Honea et al. 2005). Other regions are also strongly involved in the disease, such
as the medial frontal cortex (Bora et al. 2011), which has been proposed as a key region.
Ellison-Wright and Bullmore (Ellison-Wright and Bullmore 2010) performed a meta13
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
analysis of 42 VBM studies of schizophrenia, where they found that the distribution of GM
volume reductions was wider in schizophrenia than for other mental diseases, such as
bipolar disorder, affecting frontal, temporal, cingulate, insula and thalamus. Postmortem
studies support all these findings (Brown et al. 1986; Pakkenberg 1987; Bogerts et al.). All
this information leads to a conclusion that GM is a tissue highly involved in the disease,
and that the pattern of brain damage may be more global than neuroimaging findings so
far suggest, hence that this is not sufficient.
Finding specific morphometric alterations associated with a particular disease is a
widespread goal in neuroimaging research. It has been performed in hundreds of studies,
mainly by applying the Voxel-Based Morphometry (VBM) technique (Wright et al. 1995;
Ashburner and Friston 2000; Ashburner and Friston 2001) for comparing brain
anatomies. In brief, VBM involves preprocessing the original MR images, by segmenting
them into different tissue types. These are then aligned into the same anatomical space.
Next, a statistical analysis is performed to enable a comparison among populations. VBM
has contributed enormously to the field of neuroscience, and in particular to the
knowledge about schizophrenia. However, it is a mass-univariate approach, which
assumes voxels are independent. The interconnected nature of the brain suggests that this
may not be the most biologically plausible assumption to make. Many neuroimaging
advances now focus on multivariate analysis frameworks, with many recent developments
based on pattern recognition and other machine learning approaches. Powerful machine
learning techniques from other fields have been adopted to obtain a more accurate
understanding of the different processes that occur in the brain. Having a more accurate
model may allow more rapid translation from basic research into clinical applications.
This is the role of multivariate techniques in neuroimaging (Ashburner and Klöppel 2011).
Such applications yield interesting predictions based on more accurate characterizations
of differences between populations of subjects (Schrouff et al. 2013; Sabuncu and
Konukoglu 2014). In the last ten years, pattern recognition techniques have been widely
applied to structural data, mainly for predicting clinical status at the individual level
(Klöppel et al. 2008; Costafreda et al. 2009; Klöppel et al. 2012; Nieuwenhuis et al. 2012;
Mourao-Miranda et al. 2012).
Nowadays, brain imaging researchers aim to collect the largest possible number of
subjects. Studies attempt to obtain findings that can generalize, for instance differences
between populations or the impact of a biomarker, etc. Successful multivariate methods
do not necessarily localize differences, but instead aim to capture the patterns of
difference that best separate subjects into groups, or predict some continuous variable of
interest. Although useful for analyses that attempt to localize differences, the widely used
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
assumption of independence among the anatomy of different brain regions is not really
biologically plausible. If this assumption is removed, greater predictive accuracy may be
possible. For example, age or gender differences are not localized to any particular brain
region. Instead, there is a pattern of differences that are distributed throughout the brain.
Studies based on localizing differences only show the most relevant aspect (like the tip of
an iceberg) but they can lose important information pertaining to patterns of relationships
among brain regions. A pattern recognition approach attempts to learn a relationship
between feature data and their corresponding labels. The algorithm, after learning such a
relationship, should be able to predict the label for new data cases.
Many different algorithms for pattern recognition analysis are available (Schrouff et al.
2013). For this thesis, Gaussian processes approach for classification and regression was
chosen (Rasmussen and Williams 2006). Gaussian Processes (GP) are kernel-based
approaches, set in a Bayesian framework. They achieve similar performance to Support
Vector Machines (SVM) for neuroimaging data (Schrouff et al. 2013) with the advantage
that they make probabilistic predictions. These supervised algorithms learn the mapping
between the input (data features) and its output (labels) from a set of training data.
Depending on whether the output is continuous or discrete, it would be respectively a
classification or a regression problem. GP processes are more thoroughly presented in
section 1.3.
There are many different procedures to model data for classification and regression. Most
of these approaches involve pre-processing structural MRI scans in the same way as for a
conventional VBM analysis (Wright et al. 1995; Ashburner and Friston 2000) but then
applying a pattern recognition technique. These kind of analyses require some form of
characterization of inter-subject neuroanatomical variability (more detailed explanation
about these characterizations from MRI preprocessed data in sections 1.2 and 1.4). Much
of this variance among brain images can be characterized by shape modeling
(computational anatomy), where the accuracy of inter-subject registration plays a
significant role in terms of the findings and their interpretability (Ashburner and Klöppel
2011). Conclusions from any particular study depend heavily on how the data are
modeled, and the assumptions underlying those models. If data are imprecisely modeled
or the characterization used does not incorporate key information, this may result in poor
predictions. Obtaining informative image features is an area of interest for many using
pattern recognition in clinical research.
The use of suboptimal features for pattern recognition limits the accuracy with which
predictions may be made. Each feature encodes information about biological processes,
mental or neurodegenerative diseases, etc. However, each process or specific disease
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
involves and alters each bit of brain anatomy in different proportions. No Free Lunch
theorem states that prior knowledge about what is likely to be informative should be
essential for pattern recognition. This scenario leads to the strong motivation of exploring
different features, how they encode information and whether it is possible to generalize
about them.
Regarding accuracy in modeling, it is being established step-by-step in the VBM-type
preprocessing. In VBM, the outputs from segmentation are often used to drive image
registration. If the segmentation does not work accurately, the next step cannot be
accurate either. Hence the interest in the accuracy of such automated computational tools
is increasing.
Hundreds of studies have used structural MRI data, mostly for VBM (Wright et al. 1995;
Ashburner and Friston 2000). Pre-processing structural MRI for VBM usually entails
applying a pipeline of different algorithms to model the images. First step involves
segmenting the images in order to identify the tissues of interest. These are mainly grey
matter (GM) and white matter (WM) tissue classes. Tissue classes are then spatially
normalized and smoothed to enable statistical comparisons. Reliable findings depend on
reliable registered tissue classes. In VBM, the outputs from segmentation are involved in
registration. If segmentation is inaccurate, the next step cannot be accurate either. Hence
the accuracy of the final preprocessed data is dependent on each step of the processing.
Several questions arise when a VBM has to be carried out. The first one is about which
software to use. In the neuroimaging field, the two most widely used software packages
are FSL (Analysis Group, FMRIB. Oxford, UK) and SPM (Wellcome Trust Centre for
Neuroimaging, UCL Institute of Neurology. London, UK). Both, FSL and SPM, have
implemented different approaches for VBM pre-processing. These share some
commonalities, but there are also a number of differences. For image segmentation, the
SPM package implements a method based on fitting mixtures of Gaussians to the image
intensities (Ashburner and Friston 2005). This is combined with an atlas-guided approach,
in which a warping from the atlas to each image is performed. In that way, the
characteristic space of intensities and the spatial information of the image are both
combined. The approach in the FSL package is similar, but also includes a Markov Random
Field, which models interactions between voxels and their nearest neighbors (Zhang,
Brady, and Smith 2001). There are many relevant differences between these two options,
although there are some commonalities. Both SPM and FSL are assembled in a Bayesian
framework. In both cases the problem is formulated as MAP estimation. Finally, the model
fitting is performed by the Iterative Conditional Modes and the Expectation Maximization
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
algorithms. These two approaches for brain image segmentation are briefly described,
with emphasis on commonalities and differences in section 1.1.
Each of these two packages for VBM-type preprocessing is based on assumptions and,
even though their reliability is assumed, results may differ. This leads to the consideration
that differences in segmentation and modeling may be biased in some way. A strategy to
address this situation involves testing the reliability of each of those software tools.
Reliable findings depend on reliably registered tissue classes. This has been explored for a
wide range of algorithms for brain image segmentation, and using different strategies on
available datasets (Tsang et al. 2008; Helms et al. 2006; Bouix et al. 2007; Lalaoui L. &
Mohamadi T. 2013; Valverde et al. 2015). Accurate brain tissue segmentation is crucial for
reliable VBM or pattern recognition analyses.
One of the main purposes of the current thesis is the application of improved
methodologies for clinical research. Obtaining trustworthy features from structural MRI
data, regarding the accuracy in modelling and the information encoded, becomes a need
for pattern recognition studies in schizophrenia and other diseases. A step in this direction
would contribute to the implementation of these techniques in daily clinical practise.
1.1 Algorithms for brain image segmentation
Most segmentation algorithms give results that are acceptable enough to be used by many
researchers around the world. However, tissue class images obtained from different
algorithm models can differ in very subtle ways. It would be exceptional to obtain a pair of
identical GM maps, if they have been estimated using two different algorithms.
In this thesis, three different implementations for brain image segmentation:
i.
FAST v4.1 (FMRIB’s Algorithm Segmentation Tool) implemented in FSL.
ii. Segment: the Unified Segmentation implemented in SPM8.
iii. New Segment: the New Segmentation implemented in SPM8.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
1.1.1 Comparative description of the models steps
SPM
FSL
1a.
1b. Brain Extraction
SPM does not require brain extraction before FAST requires skull stripped images. Brain
initializing any segmentation algorithm.
Extraction Tool (BET) is used for this purpose.
The Intensity Histogram is processed to find the
image intensity effective range. Then, a rough
threshold t is determined, which attempts to
distinguish between brain and background, air
and skull.
Then, the brain surface is modeled by a
tessellated surface. Beginning witha tessellated
sphere placed in the center of gravity, the
algorithm deforms it to identify the optimal
surface (Smith 2001).
A common approach for two different ways of segmentation
The Finite Mixture (FM) model isset within a Bayesian framework, and used to model voxel
intensity distributions. The FM model assumes that information about the properties of voxels is
spatially independent and it does not take into account any spatial information.
P( yi | k )  f ( yi ; k );
(1.1)
P(ci  k )   k
The intensity value of voxel i is denoted by yi, and k represents the index of the Gaussian (cluster),
which explicitly is defined by their parameters θk. Then, γk is the mixing coefficient that accounts for
the proportion of voxels that corresponds to this kth Gaussian.
In the Bayesian framework, the probability of an entire data set is given bythe next expression,
I
K

P( y |  ,  )    P( yi | ci  k ,k )  P(ci  k ) 
i 1  k 1

(1.2)
With the terms introduced in (1.1), this becomes
I
K

P( y |  ,  )     f ( yi ;k ) k 
i 1  k 1

(1.3)
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
However, not considering spatial information is a downside.To overcome this issue, bias correction
models and some spatial properties, or constraints, have to be incorporated. These
implementations are based in two different models that are described below.
3a. UNIFIED SEGMENTATION
3b. FAST
& NEW SEGMENTATION
The model involves:
Same generative model involves:

Tissue class segmentation

Tissue class segmentation

Registration

Bias correction

Bias correction
Using the Markov Random Field (MRF)
Using a Finite Mixture (FM) model
by
(1) Spatial information is incorporated by
incorporating tissue probability maps (TPMs)
defining a neighborhood system around each
into the model by modifying the stationary
voxel. The MRF properties can be described by
mixing proportions. In the original “Unified
factorizing according to
(1) Spatial
information
is
included
Segmentation” implementation, these TPMs are
GM, WM and CSF. In the “New Segmentation”
P( x)  0, x ; P(xi | xS i )  P(xi | xNi )
implementation, bone, soft tissue and air are
(1.4b)
added to the above mentioned tissues.
Ignoring registration, the spatial priors for
“Unified Segmentation” are given by
P( ci  k |  k ) 
 k bik
j
By multiplying each term (the clique potentials)
is possible to get the Gibbs distribution
P ( x )  Z 1e ( U ( x )) ; Z   e ( U ( x ))
(1.5b)
x X
(1.4a)
The HMRF in FAST can be described by:
 b
j ij
i 1
For the “New Segmentation” of SPM8, priors
are defined by:
 X=
 Xi ,i S which
is the hidden MRF, with
prior distribution p(x).
P(ci  k | k ) bik
(1.5a)
 Y=
Yi , i  S that
is the observable random
Registration. These priors are deformable
field, with emission probability distribution
spatial
p yi | xi  for each yi .
priors.
The
deformation
parameterization in the original “Unified
Segmentation” is by a linear combination of
cosine transform bases (Ashburner and Friston
 The parameter set
  l , l  L are
used to
model the distributions.
1999). However, the “New Segmentation”uses
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
a many more parameters, and optimisation The spatial dependency is modeled by the
involves usingsome of the same technology neighborhood system p(l)    p(l | x ) ,
l
Ni
asfor DARTEL (Ashburner 2007), which has
so that modifies the FM model expression
about 700,000 parameters. In both Unified and
New Segmentation, parameters are introduced
p( yi | xN i , )   p( yi , l | xNi ,  )   f ( yi ;l ) p(l | xNi )
lL
into the previous probabilistic equations (1.1)
lL
(1.6b)
and (1.2).
Incorporating deformable tissue priors, the Assuming a Gaussian distribution of the intensity,
likelihood
equation
for
the
Unified for the entire data set, the likelihood is
Segmentation becomes

P (x | y)   

i S

I
P( y |  ,  ,  )   P( yi |  ,  ,  ) 
 ( y i   xi ) 2
1
exp  
 log  xi

2 x2i
2


     P  X 

(1.7b)
i 1



K
 ( yi  k ) 2  
1
 k bik ( )
  K
exp  


2 1/2
2 k2  
i 1 
k 1  2 

k
   k bik ( )

 k 1

(1.6a)
I
For the New Segmentation, it becomes
I
P( y |  ,  ,  )   P( yi |  ,  ,  ) 
i 1
 K
 ( yi  k )2  
bik ( )

 
exp  

2 1/2
2 k2  
i 1  k 1  2 

k


I
(1.7a)
Optimization involves minimizing the negative
logarithm of these probabilities.


K  b
 ( y   )2
1
k ik  
    log  K
exp   i 2 k

1/2
2 k
  b  k 1 2 k2
i 1

  k ik  
 k 1
I








(1.8a), and
 K
 ( yi   k ) 2  
bik ( )

   log 
exp  

 k 1  2 2 1/ 2
2 k2  
i 1

k


I
(1.9a)
(2) Bias correction assumes that noise is
(2) Bias correctionis based on a method by
added to the image and then, scaled by a bias,
Wells et al. (Wells et al. 1996). The bias field is a
as:
multiplicative vector. Then, the effect of the bias
20
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
yi  (i ni )/ i
(1.10a)
The bias model is included in the FM model by
adding a parameterization ( i
   ; where 
is a vector of unknown parameters). It modifies
field at each voxel is expressed as:
Ii  Ii* bi
(1.8b)
But it becomes an additive artifact with the
logarithm transformation.
the likelihood equation to

K
b  
 ( ( ) yi  k )2  
  log  i ( ) ik 1/2 exp   i

2

2k2
i1
k 1  2 


k

(1.11a)
log I  log I *  log b  y  y*  B
(1.9b)
I
The intensity distribution, which it is modeled as
a FM model, includes the bias field as


p ( yi | B )   g  yi  bi ;   j   P  j 
(1.10b)
j L
The objective function becomes
P ( x | y )  P ( y | x ) P ( X )   p ( yi | xi )  P ( X ) 
iS


    g  yi  bi ;  l  j   P  j    P  X 

iS  lL
(1.11b)
4.a REGULARIZATION
4.b REGULARIZATION
Regularizing penalizes the model to give more
plausible
bias
fields
and
This approach does not use any regularization.
nonlinear
deformations. The probability density of the
spatial parameters that parameterize both the
bias field and the registration parameters are
assumed
to
be
multivariate
Gaussians
distributions. Regularization of deformations is
based on their “bending energy” (Ashburner
and Friston 1999).
Model fitting by ICM and EM algorithms
In both softwares, optimization consists of minimizing their respective objective functions. The
Iterated Conditional Modes (ICM) algorithm (Besag 1986) is used to estimate each parameter,
which is subsequently updated by the Expectation-Maximization (EM) algorithm (Dempster,
Laird, and Rubin 1977; Bishop, Svensen, and Williams 1998; Neal and Hinton 1998). In this way,
when a parameter is updated by the EM algorithm, the remaining parameters are held fixed until
21
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
its own turn arrives, alternating one parameter each time.
The optimization is split in two steps the Expectation step and the Maximization step:
i. E-step: the algorithm calculates the conditional expectation.
ii. M-step: it maximizes the probability to obtain the next estimate.
Intuitively, EM is an iterative method that, given the observed data Y, alternates among estimating
the unknown parameters () and the hidden variable (class label x). The algorithm computes a
distribution over the X space, given an estimate  at each iteration, because both are strongly
inter-dependent. The objective is to maximize the posterior probability (1.12) of the parameters 
given the data Y, marginalizing over X.
 *  arg max  P  , x | y 

(1.12)
xX
For simplicity, the log probabilities are maximised:
 *  arg max logP  , Y   arg max log  P  y, x,  


(1.13)
xX
5.a Optimization
5.b Optimization
The estimation process alternates among
FAST does not use any kind of spatial information
optimizing
parameters
for segmentation. It does the model may not be
(registration, bias correction, and computing
robust enough in certain cases. For instance, in
the intensity distributions) while keeping the
those where the bias field has an important effect
others fixed (ICM).
over the data. The EM algorithm attempts to
each
set
of
For parameterization of the deformations,
the Gauss-Newton strategy is used. In the
Unified Segmentation framework, this is
relatively
straightforward
because
the
matrices involved are relatively small. In the
New Segmentation approach, there are many
more
registration
parameters
so
the
multigrid procedure developed for DARTEL
is used instead.
overcome the downside in its own specific HMRFEM framework, which incorporates the bias field
correction step in the same model.
An EM solution is sought for the dependent
variables: the bias field, the tissue classification
and the model parameters. In the E step, a MAP
estimate is made of the bias field and the class
label. In the M step, the ML allows to calculate the
parameters using the estimated bias field and the
A local optimization procedure is used, so it is
class labels obtained in the previous E step. The
necessary to establish reasonably good initial
algorithm scheme can be seen in the next table.
starting estimates. These are randomly
22
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
assigned for thecluster parameters. The
coefficients for the bias and the nonlinear
registration are set to zero (an affine
registration is first used to roughly align with
the TPM, by optimising the objective function
of D’Agostino et al. (Agostino et al. 2004).
The parameters of interest in this model,
  , , , , 
are optimized by the EM
algorithm (Bishop, Svensen, and Williams
1998; Dempster, Laird, and Rubin 1977; Neal
and Hinton 1998). Details can be seen in the
Unified Segmentation paper (Ashburner and
Friston 2005). The general framework is
similar
in
both
the
Unified
and
HMRF-EM algorithm for brain MR image
segmentation and bias field correction, from Zhang,
Brady & Smith, 2001.
New
Segmentation models.
23
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
1.2 Diffeomorphic image registration by Geodesic Shooting
One of the main purposes in image registration is the measurement and statistical study of
variations in brain anatomy. Image registration generally involves finding the set of
parameters that best encode the continuous mapping from one shape to another. There
are several approaches to do this, but they can broadly be divided into two main
categories: the small-deformation and the large-deformation approaches. The main
difference is that the first one does not guarantee that topology is preserved, whereas the
second does. Large-deformations, or diffeomorphisms, involve transformations that can
be inverted. Composing a forward transform with its inverse produces the identity
transform. This is relevant, because during the registration process inversions are
required (Ashburner 2007). Hence, large-deformation approaches are desirable to get the
best parameterization.
Early diffeomorphic registration was based on a framework that models deformations as a
“viscous fluid”, such that one shape flows to match another (G. Christensen et al. 1995; G.
E. Christensen 1994). More recently, approaches for nonlinear image registration are
based on the Large Deformation Diffeomorphic Metric Mapping (LDDMM) described by
Beg. et al. (Beg et al. 2005). Given a template image µ, an image target f can be represented
as a function of µ. The LDDMM algorithm computes a diffeomorphic transformation :
 between these images (where spatial domain 3), such that = (
curve = , defined between t[0,1], parameterizes the path by means of the ordinary
differential equation ̇ =
=
). The
(
), the diffeomorphism = =
is the identity and
is defined as the end point of the path. The equation is dependent on the velocity
vector field of the flow of the deformation,
: , and on t[0,1]. The diffeomorphism
 is obtained from
=
=∫
( )
(1.14)
The objective is to estimate a series of velocity fields , over t[0,1]. The optimal curve of
is obtained by optimizing a variational problem. The large-deformation diffeomorphic
metric mapping is obtained by minimizing
∫ ‖
‖
+
− (
)
(1.15)
where L is a differential operator. The first term minimizes the squared distance of the
deformation, which is the geodesic shortest path for the metric distance. The second term
minimizes the difference between the warped template, (
), and the individual scan f.
24
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
For this thesis, the algorithm for image registration used is based on the LDDMM
framework, but includes some additional components that enable more efficient
registration, both the number of iterations needed to achieve convergence and the amount
of memory required to encode the deformations (Ashburner and Friston 2011). This is the
Geodesic Shooting toolbox implemented in SPM12. Such an image registration model
involves learning the relative shape of a brain in a geometric sense. LDDMM is able to
encode relative form using the “initial momentum” formulation (Wang et al. 2007; Younes
2007), which is based on the conservation of momentum. The intermediate and final
configurations (deformation) may be determined from the initial conditions, which are the
spatial configuration (an identity transform
0)
and the initial velocity or momentum. It is
not necessary to optimize the entire series of velocity fields, but instead it is possible to
perform registration by only optimizing an initial velocity, v0 (development and equations
in Ashburner J and Friston K (2011).
This work involves using a concept known as “scalar momentum”. This does not have a
simple biological interpretation, as it is merely a concept from geometric mechanics. Files
encoding scalar momenta are computed from the registration outputs of the Geodesic
Shooting toolbox of SPM12. The scalar momentum is defined as
(
=
)( − ∘ )
(1.16)
Where  is the template that matches the image f, and
is the determinant of the
Jacobian of the transformation. The scalar momentum is related to the warped tissue
classes ( ∘ ), which unmodulated are difficult to interpret in a VBM analysis. However,
( ∘
modulated warped tissue classes,
), can be more easily interpreted in a VBM
as volume differences.
Scalar momenta become more complex when several tissues are aligned simultaneously.
In this case, they are not scalar fields. The scalar momentum used in the current study
involves grey matter (GM), white matter (WM) and an implicit background class BG = (1(GM + WM)), essentially can be described as:
(
−
( ))
(
−
( ))
(1 −
−
) − (1 −
( )−
( ))
(1.17)
This means that the scalar momenta encode information from the deformation fields,
associated with the GM and WM, and also the residual difference between these tissue
classes and the template. Further details about the method and the implementation are in
25
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
(Ashburner and Friston 2011). Note that in practice, even though there are three tissue
components (GM, WM and BG), the scalar momenta are reduced to two components. This
is because there is redundancy in the information, so some disk space can be saved using
the two component approach.
1.3 Gaussian Process Models
Given a dataset D = {xi ,yi}, i= 1, …, N, consisting of pairs of samples xid and labels yi, the
objective of a supervised learning algorithm is to learn a function from the data that can
accurately predict the corresponding label, f(xi) = yi, for new samples.
A GP is a generalization of a Gaussian probability distribution, understood as a process
that governs the properties of such functions. However, the aim is not only to find a
function that fits the data, but also finding that one that better fits the data. Thus the model
becomes complete when it is used in a Bayesian framework, using prior probability for
each possible function that models the data and giving higher probability to those that are
more likely to occur. In this way, over-fitting may be avoided.
In particular, GPs were initially developed for regression (Williams and Rasmussen 1996),
and can be conceptualized as a Bayesian extension of linear regression (Bishop 2006). For
the inputs in the dataset D, = (
,
( , )=
Where
(
,
=(
,…,
,
,…,
, …,
( )
), the model can be described as follows:
(1.18)
) are the basis functions of the inputs
, and
=
) is the weights vector, the distribution of w imposes a limitation on the
model, ( , ) is a linear function of the input variables governed by them. If a prior
distribution is assumed for , given by an isotropic Gaussian distribution,
( )=
( | ,
)
(1.19)
then this distribution induces a continuous Gaussian distribution over ( ).
The aim of this approach is to finally evaluate this function at a particular set of =
( ,
, …,
); i.e. the training sample described as input in D. Those function values
related to the input samples are described in y with components (
), (
), …, (
).
Then, this vector can be expressed as
=
Where
(1.20)
is the matrix that encompasses the basis functions, Φ
=
(
). A mean and
covariance describe a Gaussian distribution of y. These are given from the prior
probability of w due to the relationship between y and w in (1.19), by
26
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
[ ]=
[ ]
[ ]= [
]=
(1.21)
[
]
=
=K
(1.22)
Where the elements of K come from the available basis functions
=
(
) =
,
(
)
(
). (1.23)
The hyper-parameter α represents the precision of the distribution of
and corresponds
to the inverse of σ2. K is the covariance function, also known as kernel function, which
becomes directly dependent on the input sample.
In general, a GP is defined as a Gaussian probability distribution over the functions ( )
evaluated at a specific set of points (training samples), such that it jointly also fits a
Gaussian distribution (Bishop 2006).
In summary, a GP model can be specified by a multivariate Gaussian distribution with a
mean vector and covariance matrix:
~ ( ( ), ( ,
))
(1.24)
Generally, prior information about the mean is not known. By symmetry it is taken to be
zero and so, the mean of the prior over the weight values is also assumed to be zero,
p(w|α). The GP view is then completed by estimating the covariance between any pair of
input sample by means of the kernel function as
[ (
) (
)] = (
,
).
(1.25)
In each particular case, this kernel function can be estimated by defining a specific
relationship between samples. In the current work, as in the linear regression model
where weights follow an isotropic Gaussian distribution, the kernel function is given by
the dot product (1.23).
To apply GP to regression, the noise of the observed target values must be considered. It is
assumed that a randomnoiseterm is added to ( ), which follows a Gaussian distribution
independent of each observation (Bishop 2006).
GP for classification is an extension of GP for regression. As set out above, GP gives
predictions in the continuum, but when doing classification, the aim is to predict discrete
categories. If the output in the continuum is transformed by means of an activation
function, which gives 0 or 1 depending on the input, the predictions by a GP are adapted to
a classification problem. A Gaussian process defined over a function a(x) is transformed by
using a logistic sigmoid y= σ(a), to give a non-Gaussian stochastic process over functions
y(x) where y(0,1), as would be expected for a two-class problem with target t{0,1}.
27
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
This section only provides a brief introduction to GP in order to present the context
necessary to follow the material in this thesis. The interested reader is referred to Bishop
(2006) and Rasmussen and Williams (2006) for a more detailed explanation.
1.4 Data feature representation
As mentioned, the success of machine learning methods not only relies on the approach, it
also depends on the features used to fit the model. More powerful data features are
essential to achieve optimal performance from machine learning. Different kinds of
features can be obtained from the preprocessing commonly used for VBM analyses.
Outputs become features that can be used as inputs for multivariate techniques.
In this thesis, an assortment of images from the VBM-type pre-processing with SPM
software that may allow interesting characterizations were selected as features. Grey
matter (GM) and white matter (WM) tissue classes, also Jacobians, which encode the
volume changes from warping native images to the standard space, and different
operations and combinations of these images were explored.
Additionally, other relevant types of data were considered The VBM-type pre-processing
has improved enormously since the beginnings (Ashburner and Friston 2001). The
current methods for aligning the images of different subjects are more sophisticated and
accurate than a few years ago (Klein et al. 2009; Ashburner and Miller 2015). Some of
them allow different representations of image shapes, which may be useful for pattern
recognition. In that respect, scalar momenta are candidate to become interesting features.
These images, even though do not have biological interpretacion, may encode key
information about inter-subject anatomical differences.
28
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
2. Objectives
The main objective of this thesis is to obtain reliable and accurate features from structural
MRI data for pattern recognition studies in schizophrenia, which should contribute to the
application of improved methodologies in clinical research. To accomplish the main
objective, the following specific objectives are posed:
(1) Determining, from among the most used methods for brain tissue segmentation,
which algorithm produces the most reliable grey matter (GM) segments with
respect to a defined ground truth.
(2) Finding a class of features from structural MRI data that is relatively efficient,
irrespective of whether the target is discrete or continuous, for pattern recognition
studies. Image data from healthy subjects are used in order to predict
demographic variables, such as age and gender. Features that are aimed to be
studied are those obtained from the VBM-type of preprocessing: tissue classes
scaled and non-scaled by the Jacobians, Jacobians, divergence of velocities and
scalar momenta.
(3) Exploring the relationship between features from preprocessed MRI data and
smoothing.
(4) Designing how total intracranial volume (TIV) can be introduced in the features
from modulated data and studying how it influences the performance of
predictions in modulated tissue classes.
(5) Verifying whether or not GM provides the best feature for predicting
schizophrenia.
(6) Determining the optimal amount of image smoothing for predicting schizophrenia.
(7) Testing whether the types of feature that best predict demographic variables in
healthy subjects are also best for predicting schizophrenia.
29
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
2.1 Roadmap
This thesis is divided into three studies, designed to accomplish the objectives presented
above.
Study 1
A comparison between three different segmentation algorithms is performed. These
algorithms are “Unified Segmentation” (US) and “New Segmentation” (NS) from the SPM8
package, and FAST from the FSL package. A publicly available data set, which includes
manually segmented tissue classes by experts, was used. A detailed comparison between
algorithms and ground truth was conducted using different methods for testing the
reliability of each algorithm with respect to the “gold standard” segmentations. With this
study objective (1) can be fulfilled.
Study 2
This study involves applying the Gaussian Processes machine learning approach to a
number of sets of features derived from same subjects’ preprocessed MRI data. The age,
body mass index and gender of all subjects was predicted in order to find an effective
feature representation of image data from multiple subjects, such that pattern recognition
methods may be made more accurate. Predictive accuracy was explored using a variety of
image features, which had been spatially smoothed over a wide range of full-width at half
maximum (FWHM). Also a novel method for including total intracranial volume (TIV) into
the features was attempted. With this work, objectives (2), (3) and (4) can be evaluated.
Study 3
This study consists in applying conclusions from the previous evaluations to
schizophrenia. Our hypothesis was that image features that worked well in study 2 would
also work well for predicting schizophrenia. With this study, objectives (5), (6) and (7)
were to be answered, as well as accomplish the main objective of this thesis.
30
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
3. Study 1: Influence of segmentation
model in VBM-type preprocessing
Nowadays, the interest in the accuracy of automated computational neuroanatomy tools is
increasing. Hundreds of studies have used structural MRI data, mostly for Voxel-Based
Morphometry (VBM) (Wright et al. 1995; Ashburner and Friston 2000; Ashburner and
Friston 2001). Pre-processing structural MRI for VBM usually entails applying a pipeline of
different algorithms to model the images. First step involves segmenting the images in
order to identify the tissues of interest. These are mainly grey matter (GM) and white
matter (WM) tissue classes. Tissue classes are then spatially normalized and smoothed to
enable statistical comparisons. Reliable findings depend on reliable registered tissue
classes. In VBM, the outputs from segmentation are involved in registration. If
segmentation is inaccurate, the next step cannot be accurate either. Hence the accuracy of
the final preprocessed data is dependent on each step of the processing.
Several questions arise when a VBM has to be carried out. The first one is about which
software to use. In the neuroimaging field, the two most widely used software packages
are FSL (Analysis Group, FMRIB. Oxford, UK) and SPM (Wellcome Trust Centre for
Neuroimaging, UCL Institute of Neurology. London, UK). Both, FSL and SPM, have
implemented different approaches for VBM pre-processing. These share some
commonalities, but there are also a number of differences.
For image segmentation, the SPM package implements a method based on fitting mixtures
of Gaussians to the image intensities (Ashburner and Friston 2005). This is combined with
an atlas guided approach, in which a warping from the atlas to each image is performed. In
that way, the characteristic space of intensities and the spatial information of the image
are both combined. The approach in the FSL package is similar, but also includes a Markov
Random Field, which models interactions between voxels and their nearest neighbors
(Zhang, Brady, and Smith 2001).
There are many relevant differences between these two options, although there are some
commonalities. Both SPM and FSL are assembled in a Bayesian framework. In both cases
the problem is formulated as MAP estimation. Finally, the model fitting is performed by
the Iterative Conditional Modes and the Expectation Maximization algorithms.
31
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
3.1 Motivation & Objectives
Two different theoretical frameworks entail different algorithm implementations, leading
to subtly different tissue class images arising from FSL and SPM. This study focuses in
quantifying those differences. For this purpose, a public dataset has been used. This
dataset has been selected because tissue classes segmented by experts are available. These
manually segmented tissue classes were used as the “ground truth”.
Differences due to methodology and systematic bias inherent to the algorithms can be
influenced by additional factors. Poor quality images, artifacts, pathology, and anatomical
variability in general, can cause miss-segmentation. Images used in this study have poor
quality, exhibit low contrast and relatively large intensity gradients. Segmentation
algorithms must face these additional difficulties.
The objective of the current study is to determine which algorithm gives tissue classes
more similar to the ground truth. This decision is made by (1) evaluating the influence of
the differences between approaches, (2) detecting systematic errors, if they exist, caused
by each segmentation algorithm, and (3) quantifying similarities between resulting tissue
classes from each segmentation method and the ground truth.
3.2 Material & Methods
This study focused on the comparison between two segmentation approaches, by SPM and
FSL. For this purpose, both algorithms were applied to the same public dataset. This
dataset also included manually segmented tissue classes that were used as gold standard.
The work is divided into two parts. First, preliminary evaluations were performed in order
to define the initial requirements and how they may interfere in the segmentation process.
Hence, the effects ofthe manual reorientation necessary for SPM, and the skull stripping
essential in FSL, were explored.
Second, the pipelines were conducted and evaluated at each step for finally quantifying
differences at the final stage. Each segmentation process was carried out in identical
conditions and default settings were used for each software.
3.2.1 Data
The evaluation was performed with 20 normal MR brain scans provided by the Center for
Morphometric Analysis at Massachusetts General Hospital. Scans are available at the IBSR
32
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
web site1. These images have been manually segmented by experts, and the segments are
also available at the IBSR web site. Ground truth GM, WM and CSF were compared with the
tissue classes estimated by the automated methods. These images involve certain level of
difficulty, there are scans that contain considerable acquisition artifacts as well as
irregularities.
Data acquisition
The high resolution structural T1-weighted MRI data were acquired ona 1.5 Tesla GE
Signa scanner (General Electrics Medical Systems, Milwaukee, Wis.), with the following
acquisitions parameters: Matrix size 512 × 512; 180 contiguous axial slices; voxel
resolution 0.47×0.47×1 mm3; echo (TE), repetition (TR) and inversion (TI) times, (TE/
TR/ TI)= 3.93ms/ 200ms/ 710ms respectively; flip angle 15 degrees).
3.2.2 Software
Comparison was carried out between:
▫
FSL 4.1.5 - Two scripts from FSL-VBM v1.1were used: the BET2.1 (fslvbm_1_bet),
and the FAST tools (fslvbm_2_template).
▫
SPM8 - Segmentation for VBM pre-processing includes two different approaches:
“Unified Segmentation” and “New Segmentation”.
3.2.3 Preliminary evaluations
Differences between software pipelines at various stages were explored. These stages
relate to how data should be prepared: skull stripping that is necessary for FSL
segmentation and manual reorientation of the images recommended for SPM.
Manual realignment
Prior to the actual segmentation in SPM, an affine registration between tissue probability
priors and the images to segment is performed. The idea behind the manual positioning is
to make the segmentation more robust to local optima from this registration. In the
“Unified” and “New Segmentation”, manual reorientation is recommended. This involves
reorienting images so that the anterior commissure (AC) is close to the origin of their
“world” coordinate system, approximately with same orientation asthe ICBM templates
supplied with SPM. A preliminary test to visualize this effect was explored: the SPM8
1
Internet Brain Segmentation Repository | www.cma.mgh.harvard.edu/ibsr/
33
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
implementations of “Unified Segmentation” and “New Segmentation” were used to
segment non-reoriented data.
Brain Extraction Tool
VBM with FSL was performed using the FSL_VBM v1.1 tool. The pipeline of this tool
consists of three steps: fslvbm_1_bet, where the brain is extracted from the T1-weighted
images; fslvbm_2_template, in which GM tissue class is segmented and a GM template is
created, and fslvbm_3_proc, the non-linear registration of the GM images is performed.
The first step (fslvbm_1_bet) conducts brain extraction, and it is done by BET. This tool is
provided with several options for skull stripping. Depending on the option, extracted
brains may differ. For instance, automatically segmented brain may include part of the
neck, eye balls, etc. On the contrary, tissue of the cortex may be wrongly removed. In
addition, the accuracy depends on whether the “standard” (runs BET2) or “robust” (runs
BET2 twice) forms of the procedure are run. Subsequent GM segmentation may dependon
the prior brain extraction.
A preliminary test was conducted to explore the role of BET in a VBM. Two trials were
performed with the ISBR dataset:
First trial: Brain extraction of the IBSR dataset
The most used commands available for fslvbm_1_bet were explored in the “standard”
way. The options explored were:
(1) fslvbm_1_bet -b: BET works by default.
(2) fslvbm_1_bet -N: This option is more restrictive, and is recommended when images
include part of the neck.
(3) fslvbm_1_bet -N -f 0.5: This command fixes the fractional intensity threshold to 0.5,
instead of default 0.4, which is less restrictive.
(4) fslvbm_1_bet -N -f 0.5 –R: Adding –R, BET runs a more robust brain centre estimation.
Second trial: Segmentation validation engine (SVE)
The second trial was conducted by means of the segmentation validation engine2 (SVE).
This is an online resource for validation of brain segmentation methods (Shattuck et al.
2009). The method involves extracting the brain from a dataset that it is provided for this
purposewith the tool selected by the user. This dataset is the LPBA40 (Shattuck et al.
2
Segmentation Validation Engine | http://sve.loni.ucla.edu/archive/
34
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
2008), and consist of 40 T1-weighted MRI volumes stored in NIFTI format. It has been
used in several studies, such as the creation of the LONI Probabilistic Brain Atlas. Data
were facilitated by the UCLA Laboratory of Neuro Imaging (LONI) for analysis following
IRB approved procedures of both NSLIJHS and UCLA. For the current validations, data
were not pre-processed.
Procedure: LPBA40 data were skull stripped using the same commands as in the first
trial, outcomes were returned and an evaluation metrics was computed. The evaluation of
differences was done by a metrics used for comparing binary segmentations of the same
structures.
Using different measures from the data, success and error rates and other metrics often
used in these kinds of comparisons were estimated. The Jaccard similarity coefficient is
one of the most used for quantifying similarities and differences between images, and it
was used in the next analyses.
Jaccard similarity coefficient
Given a pair of images, A: automated GM segment and M: manual GM segment, each one
with n binary attributes, the Jaccard coefficient is a measure of the overlap between A and
M. Each attribute of A and M can either be 0 or 1. The total number of each combination of
attributes for both A and M are specified as follows:
▫
M11 represents the total number of voxels where A and M both have value 1.
▫
M01 represents the total number of voxels where A is 0 and M is 1.
▫
M10 represents the total number of voxels where A is 1 and M is 0.
▫
M00 represents the total number of voxels where A and M both have value 0.
Each voxel must fall into one of these four categories, the sum of all them are the total
number of voxels (n):
M11 + M01 + M10 + M00 = n
(2.6)
The Jaccard similarity coefficient is calculated as
J ( A, M ) 
| A M |
| M 11 |

| A  M | | M 01 |  | M 10 |  | M 11 |
(2.7)
35
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.1 – Pair of images, A and M. Representation of the overlap between images.
The Jaccard index quantifies similarity between images.
3.2.4 Experimental design
After preliminary tests, the main body of the study was performed. Experimental design is
divided into two parts. Part 1 is performed in the native space, and Part 2 is conducted in
the stereotaxic space. Figure 3.2 describes an outline of these two parts. Each box
represents one stepin the processing pipeline.
36
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig 3.2– Part 1 involves the comparison in native space (dark grey). Part 2 is conducted in the same
anatomical space, it involves a registration process (pale grey).
Preliminaries
In the preliminary evaluations, the effects of manual reorientation on SPM’s
segmentationand the skull stripping necessary for FSL were explored. These evaluations
were conducted for establishing initial conditions in the current study.
37
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
The IBSR dataset was manually reoriented. This process does not interfere with the FSL
processing. Then, the dataset used in all the pipelines with SPM and FSL was the same.
Manual reorientation of the IBSR scans was done jointly with their respective manual
segmentations. The comparison between automatic segmentations and their associated
gold standards was conducted in the original and the reoriented position.
On the other hand, skull stripping with fslvbm_1_bet –N was conducted in the pipeline for
segmentation using FSL.
Part 1: Native space
The aim of this section is to quantify differences that occur at the individual level due to
the processingin the native space. Analyses were carried out using both FSL and SPM with
the following tools:
1. BET (fslvbm_1_bet -N) + FAST (FSL VBM v1.1 in FSL 4.1.5)
2. “Unified Segmentation” (SPM8)
3. “New Segmentation” (SPM8)
Fig. 3.3 - Design of PART 1 trial.
38
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Evaluation of GM tissue class
The three segmentation processes were run using the re-oriented IBSR dataset. From all of
them, the resulting GM tissue classes were selected and binary masks were created. In line
with that, other masks were created from the manually segmented GM tissue classes,
which were considered the gold standard (GS) masks.
The comparison between GS masks and the GM masks obtained from the three pipelines,
was made in the native space. Thus, masks from automatically segmented tissues were
transformed back to the native position. Header matrices were checked to ensure that
they were identically positioned.
Differences between the GM segments from each pipeline and their respective GS masks,
were calculated using the Jaccard similarity coefficient (described above in the SVE
section).
Part 2: Customized anatomical space
In this part, the averaged differences between segmentations from each of the pipelines
and the gold standard were computed. For this purpose, data were transformed to the
same anatomical space. Next, differences between performances from each pipeline, with
respect to the manual gold standard,were calculated and compared. This procedure allows
any systematic errors to be detected.
Fig. 3.4 –Design of Part 2
39
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Registration
Registration of the GM data was carried out using Dartel (Ashburner 2007). Normalization
parameters were estimated once, from pipeline 3 using “New Segmentation”. It allowed
the rest of sets to be normalized, because the same data were used in the other pipelines.
When required, the “New Segmentation” algorithm generates additional files that can be
used to drive registration to a common anatomical space. These files are rigidly aligned
versions of the GM and WM, which have been down sampled to isotropic 1.5mm
resolution (“Dartel imported files”).
Dartel (Ashburner 2007) was used to estimate accurate spatially normalizing
transformations. Registration was driven by simultaneously aligning GM with GM, and WM
with WM, using the default regularization and optimization settings. This approach
especially improves the alignment of smaller inner structures. The version in a former
release (SPM5) has been shown to outperform other approaches to spatial normalization
(Klein et al. 2009).
Warping of tissue classes
The files encoding the spatial transformations (“flow fields”) were used for warping the
data obtained from the three pipelines. Each tissue class (GM, WM and CSF) in the native
space was warped with its respective flow field. Also the manual gold standard segments
were warped.
Evaluation of the normalized tissue classes
Binary masks were created from the warped tissues following same procedure described
in part 1. Then, GM masks were subtracted from the gold standard GM masks, which were
also in the same anatomical space. Resulting images consisted of the warped false
positive/negative images associated with each subject. A scheme of this process is
outlined in figure 3.5.
40
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.5 –Outline of the process for creating warped false positive-negative images.
For computing differences:
i.
Statistics. Voxels from false positive/negative images were counted. With
numerical data, a two sample t-test was performed pair by pair, for false-positives and for
false-negatives.
ii. Jaccard similarity coefficient. Differences between the masks from the
automated algorithms and their respective GS masks were calculated using the Jaccard
coefficient index, and a table with the results is presented in Table 3.3.
iii. Mean images. From the false positive/negative images, a mean image was created
for each set of false positives/negatives. These average images encode information about
the general performance of each algorithm and if any associated systematic errors.
However, these mean images may be biased due to a local fluctuation caused by a subject.
The contribution of one subject to the mean may not be representative of the performance
of an algorithm. In order to regularize this effect, the mean images were threshold. The
original mean images had voxels from -1 to 1. Voxels with a value 1 and -1 were involved
in 100% of the sample. If the value was 0.8, then 80% of the sample contained such voxel
in the false positive-negative images, if the value was 0.5, it was the 50% and so on.
Differences are more consistent when mean images are filtered. Contributions of 80% and
50% were explored. Cleaner mean images were more representative of the automated
segmentation algorithms.
41
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
To determine whether the areas that appeared in the mean images were involved,either in
false positive or in false negative, thresholded mean images were split, by separating false
positives and false negatives. Locations of the areas are detailed in Table 3.7.
iv. Finally, the density of voxels at the locations detailed in Table 3.7 were computed,
in Table 3.8. Mean images from 50% and 80% of sample contribution were created. It was
calculated from mean images that contained only voxelvalues associated with the 50% and
80% of sample contribution. Density was estimated by obtaining the volume of these files,
and dividing it by the number of voxels included in the respective mean, 50% or 80%.
42
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
3.3 Results
3.3.1 Preliminary evaluations
Manual realignment
Unified Segmentation
Using “Unified Segmentation”, the segmentation failed for all of the IBSR data set without
reorienting (Fig. 3.6 - top).
New Segmentation
In many cases this segmentation showed very different results compared to those
obtained by the Unified Segmentation. New Segmentation resolved the lack of positioning
in many cases. The bottom of Fig. 3.6 shows the same subject segmented by New
Segmentation, with and without reorientation.
Fig 3.6 – Anatomical image (Ctrl. 12), and its respective GM segments by US without reorienting, and
by NS without reorienting and reorienting.
43
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.7- Same subject (Ctrl. 13)) segmented by NS:Reoriented (left), and non-reoriented(right).
Although performance was better than for “Unified Segmentation”, lighter deformations
were found. The origin of these distortions lies in the affine registration that it is done to
initialize the segmentation algorithm. The New Segmentation by itself does not have
problems with the orientation, but a poor reorientation entails the risk that the affine
registration algorithm could find a local optimum instead of the global optimum.
Actually, when the New Segmentation does not work the effect is pretty clear. It can be
tested by introducing -1, to rotate one axis, or by rotating the image π or π/2 around the z
axis (1.5702 radians at the raw).
Fig. 3.8 – Same subject (ctrl. 20) segmented by NS: reoriented, and rotated π/2.
44
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Reorientation prior to running the segmentation seems necessary to avoid problems.
Centering the origin at the anterior commissure, positioning the axis within about 3 cm
and 15° degrees usually enables a good performance of the algorithm.
Brain ExtractionTool
For the IBSR dataset, the performances of different brain extraction settings were
assessed:
(1) fslvbm_1_bet -b : Tissue from neck was not eliminated.
(2) fslvbm_1_bet -N : Appeared more restrictive than (1). Results did not show extra brain
areas, brains seemed well extracted.
(3) fslvbm_1_bet -N -f 0.5 : Results were similar to (2) but this option seemed more
intrusive in the extraction at boundaries.
(4) fslvbm_1_bet -N -f 0.5 –R : Results were similar to the both above (2) and (3).
Fig. 3.9- Performances using different fslvbm_1_bet settings. Same IBSR subject (Ctrl. 20).
Last two settings showed very restrictive results after visual inspection, which can entail
the risk of removing some tissue that should be included in a VBM analysis. On the other
hand, including extra tissue that is not assumed to be GM is not ideal either. This happened
using fslvbm_1_bet –N, which failed in 7 of the 20 cases. These seven subjects were finally
skull stripped by giving the origin of coordinates, where the center of mass was visually
estimated. In those cases, instead of “-N”, another command was used, “-B”, which
attempts to reduce image bias and residual neck voxels.
45
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.9- BET by fslvbm_1_bet –N failed in two subjects. Whole brain and skull stripped images.
Segmentation validation engine (SVE)
A binary mask was created from each of the segmented LPBA40 images, and these masks
evaluated. Projection maps were computed from the false positive and false negative
values for each segmentation result. For the validation process, resulting false positive and
false negative were re-mapped to a common atlas space based on the LPBA40. Then, SVE
averaged these maps across the 40 subjects.
Dice coefficients, Jaccard indices, sensitivity and specificitywere computed from outputs,
and results for each of the BET settings are displayed in the tables and in Figures 3.10 to
3.13.
Areas that appear brighter indicate a larger number of false negative voxels, indicating
that the removal of those areas disagreed with the manually-labeled ground truth.
46
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.10- SVE output of the fslvbm_1_bet –b option.
Fig. 3.11- SVE output of the fslvbm_1_bet –N option.
47
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.12 - SVE output of the fslvbm_1_bet –N –f 0.5 option.
Fig. 3.13- SVE output of the fslvbm_1_bet –N –f 0.5 –R option.
48
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
The best results were obtained using fslvbm_1_bet –N, where the Jaccard indices and Dice
coefficients were much higher than in the other cases.
Results obtained from the two lasts settings showed similar results. A detailed inspection
of the images showed that there were no large differences between skull-stripped images
from these two options. So, adding –R did not result in amore restrictive extraction in this
data set.
The results largely agreed with those obtained with the ISBR dataset, and both trials
suggested that the “–N” setting was most suitable.
3.3.2 Experimental design
Part 1: Computing differences in native space
Differences between sets of masks from each pipeline were computed. After subtracting
automated GM tissue class masks from GS masks of GM, the resulting images contained
only voxels with value -1, 0 or 1.
▫
Voxels where the algorithm assigned more tissue in the automated GM segment than
in the gold standard GM segment were considered false positive (1, colored in white).
▫
Where the gold standard GM segment contains more tissue than the automated
segment was considered a false negative (-1, colored in black).
49
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.14 – Same subject binary masks obtained from a.1) FAST, b.1) NS and c.1) US, and their
respective difference images, obtained by subtracting these masks to their respective GS mask: a.2)
FAST - GS, b.2) NS- GS and c.2) US- GS. (Subject 100_23)
50
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.15- False positive/negative images. Between FAST and the Gold Standard: where the
algorithm assigned more tissue than the manual is in white, where the algorithm assigned less tissue
than the manual is colored in black.
51
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.16- False positive/negative images. Between NS and the Gold Standard: where the algorithm
assigned more tissue than the manual is in white, where the algorithm assigned less tissue than the
manual is colored in black.
52
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.17- False positive/negative images. Between US and the Gold Standard: where the algorithm
assigned more tissue than the manual is in white, where the algorithm assigned less tissue than the
manual is colored in black.
53
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Resulting false positive-negative images allowed detecting regions where the algorithms
systematically over- or under- determined certain amount of tissue.
Fig. 3.18- Detail from images of the differences for (a) FAST, (b) NS and (c) US. (Subject 110_3)
The number of voxels equal to 1 (considered as false positives), and the number of voxels
equal to -1 (false negatives) were counted in order to evaluate these differences
statistically.
54
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
FAST
NS
US
IBSR code
1
-1
1
-1
1
-1
100_23
17226
69347
20711
69055
27824
64359
110_3
24151
77897
24286
69988
35448
57253
111_2
26660
74047
33608
70046
39583
64278
112_2
18706
68152
21164
64466
26309
59408
11_3
23057
93879
26990
95554
36157
86420
12_3
42335
96007
33152
75120
38433
76471
13_3
36761
68324
30156
66796
42143
57850
15_3
19629
79852
21228
66749
17097
79708
16_3
13193
69743
19180
64355
18844
62468
17_3
10187
71695
19769
54872
22141
55191
191_3
14917
67485
21831
64092
26900
64450
1_24
10878
64136
18546
47511
23259
50060
202_3
17022
72303
24090
59173
34674
56883
205_3
15903
67878
24357
61754
33254
66244
2_4
17176
65348
23511
53175
26816
48297
4_8
14218
56574
20222
50567
23917
44962
5_8
20586
82838
25564
62342
25013
62227
6_10
25997
82704
25849
64248
22664
71301
7_8
11046
78196
18683
52370
24067
53624
8_4
19358
68236
24631
60651
28086
58933
average
19950
73732
23876
63644
28631
62019
st.dev.
8258
9740
4437
10415
7122
10413
T-test
1
-1
FAST vs. NS
0.0688
0.0031
FAST vs. US
0.0010
0.0007
NS vs. US
0.0155
0.6246
Table 3.1 - Table shows the number of voxels that overcame the subtraction between each algorithm
segmentation and their respective gold standard: the positives (as false positives) and the negatives
(as false negative). At the bottom: average, standard deviation, and the t-test between sets.
55
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
+1 | false positives
FAST 1
NS 1
US 1
100000
80000
60000
40000
20000
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
14
15
16
17
18
19
20
-1 | false negatives
FAST -1
NS -1
US -1
100000
80000
60000
40000
20000
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Fig. 3.19–Bar diagram of the number of voxels obtained from the subtraction between the algorithm
segment and their respective GS: a) false positives, and b) false negatives.
FAST tended to give fewer false positives than the New Segmentation and Unified
Segmentation. These differences became significant when comparing FAST and Unified
Segmentation.
However, regarding false negatives the trend was reversed, and FAST gave more false
negatives. Differences became statistically significant when comparing FAST with both the
New Segmentation and the Unified Segmentation.
56
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.20 – Box plots: (a) excess of GM by the algorithms with respect to the gold standard (voxels +1
~ false positives), and (b) lack of GM by the algorithms with respect to the gold standard (voxels -1 ~
false negatives).
Jaccard similarity coefficient
The Jaccard similarity index showed high scores in most of the subjects between the New
Segmentation and their respective gold standard. The average of the New Segmentation
Jaccard indexes achieved the most similarity with respect to the other algorithms. It was
followed closely by the Unified Segmentation, and finally by FAST.
Jaccard index
New Segmentation
UnifiedSegmentation
FAST
66.22%
65.53%
63.10%
Table 3.2 – Ranking of the Jaccard indexes of the algorithms for this sample.
57
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Next, Jaccard indexes estimation for each subject and algorithm are shown.
IBSR code
Jaccard FAST
Jaccard NS
Jaccard US
100_23
0.7084
0.7011
0.7002
110_3
0.6654
0.6910
0.7069
111_2
0.6636
0.6616
0.6674
112_2
0.6657
0.6735
0.6794
11_3
0.6824
0.6707
0.6785
12_3
0.6107
0.6872
0.6730
13_3
0.6920
0.7102
0.7114
15_3
0.5677
0.6204
0.5747
16_3
0.5841
0.5933
0.6034
17_3
0.5969
0.6491
0.6405
191_3
0.6713
0.6664
0.6522
1_24
0.6315
0.6872
0.6604
202_3
0.6839
0.7125
0.6951
205_3
0.6908
0.6918
0.6549
2_4
0.5997
0.6391
0.6519
4_8
0.6308
0.6420
0.6580
5_8
0.5316
0.6107
0.6127
6_10
0.5509
0.6276
0.6064
7_8
0.5837
0.6799
0.6583
8_4
0.6089
0.6280
0.6260
average
0.6310
0.6622
0.6556
st.Dev.
0.0521
0.0344
0.0367
algorithms
t-test | p
FAST vs. NS
0.0315
NS vs. US
0.5604
FAST vs. US
0.0927
Table 3.3 –Jaccard similarity coefficient estimated for each mask from the segments by FAST. NS and
US versus their respective GS. At the bottom. some statistical estimates; t-test became significant at
the FAST vs. NS comparison.
58
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Jaccard Similarity Coeffitient
Jaccard FAST
Jaccard NS
Jaccard US
0,8000
0,6000
0,4000
0,2000
0,0000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Fig. 3.21–Bar diagram of each estimated Jaccard coefficient
Part 2: Means in standard space from false positive-negative images
Each of the mean images shown in figures 3.22 to 3.23 was created from the 20 warped
false positive/negative maps associated with each automated segmentation processes.
White voxels represent false positives and black voxels represent false negatives.
Fig. 3.22 - Mean image of false positive-negative from FAST.
59
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.23 - Mean image of false positive-negative from New Segmentation.
Fig. 3.24 - Mean image of false positive-negative from Unified Segmentation.
60
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Table 2.4 shows the number of voxels in the mean images. False positives are in column
GM(+), and the false negatives in GM(-).
FAST
NS
US
GM (+)
GM (-)
76612
97189
111381
278951
227608
217696
Table 3.4 – Number of false positive and negative voxels in the mean images.
Fig. 3.25 – Bar diagram showing the amount of false positives (GM (+); in white) and false negatives
(GM (-); in black)in the mean image obtained from the three pipelines.
Mean images from 50% contribution
In these mean images, voxels (Figure 3.26) show where false-positives occurred in at least
50% of the samples. Differences between the mean from FSL and SPM were noticeable.
The areas where the algorithms assumed extra or lack of GM tissue were located in
different areas of the brain.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.26- Different slides of the three means with 50% sample contribution:a. FAST; b. New
Segmentation, and c.Unified Segmentation.
Next, mean images were divided into false-positive and false-negative, separately. These
images indicate the locations where algorithms over- or under-segmented the GM tissue
class (Figures 3.27 and 3.28).
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.27- Mean images from 50% of the false positives of the sample.
Fig. 3.28- Mean images from 50% of the false negatives of the sample.
False positives did not show substantial differences between algorithms. Interestingly, the
location of the areas converged. However, regarding false negatives, the areas where
algorithms incorrectly classified GM had slightly different locations.
Mean (50%)
FAST
NS
US
GM (+)
GM (-)
2790
1969
3326
21995
24727
27056
Table 3.5- number of voxels in false GM(+) and GM(-)
mean images, contribution 50% of the sample.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
false GM(+) & GM(-)
30000
25000
20000
15000
GM (+)
10000
GM (-)
5000
0
FAST
NS
US
Fig. 3.29 – Table 2.5 represented in a boxplot.
New Segmentation contained the least false positives, followed by FAST and then Unified
Segmentation. For false negative voxels, FAST contained the least, followed by New
Segmentation, and then Unified Segmentation.
Mean images from 80% contribution
The mean images of false positives/negatives with 80% of sample contribution were
created.
Fig. 3.30 – Mean imagess of 80% of the sample contribution.
The number of voxels decreased considerably. False positives and negatives were
separated and showed a similar trend to the previous case (50%). Regarding false
positives, there were no substantial differences among algorithms, and their location was
fairly consistent. Regions where false negatives occurred tended to vary across algorithms.
64
Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 3.31 – Mean images from false positives and negatives; Contribution 80% of the sample.
New Segmentation was the algorithm with the fewest false positives, followed by FAST,
and then by Unified Segmentation. FAST contained the fewest false negative voxels,
followed by Unified Segmentation, and then New Segmentation.
Mean (80%)
FAST
NS
US
GM (+)
GM (-)
321
188
358
3313
4313
3578
Table 3.6- Number of voxels in false GM(+) and GM(-) mean, concerning
the contribution of 80% of the sample.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
false GM(+) & GM(-)
4500
4000
3500
3000
2500
2000
1500
1000
500
0
GM (+)
GM (-)
FAST
NS
US
Fig. 3.32- Table 2.6 represented in a boxplot.
Location of false positive and negative
The next table reports the locations of the areas that appeared in 50% and 80% of sample
contribution to the mean images.
Table 3.7 – Location of the areas reported as false positive and negative associated to the 50% and
the 80% of the contribution to the means.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Density of voxels in false positive and negative areas
Volumeof GM in the false positive and false negative images was calculated from the mean
files, it is detailed in the table 3.8.
Table 3.8 – GM volume of false positive and negative in 50% and 80% of contribution.
Density was thought as the volume obtained from the GM that remained in the false
positive and false negative images (Table 3.7) divided by the number of voxels counted in
the corresponding false positive and false negative images.
Table 3.9 – Estimation of density of GM from false positive and negative in 50% and 80% of
contribution.
Fig. 3.33 – Bar plots of density from false positive and negative. The trend was the same in both
situations. (top-left) 50% mean and (top-right) 80% mean.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
The concept of density gave an indication of how many times a voxel was a false positive
or negative for each algorithm. In both cases, at 50% and 80% of the sample contribution,
the New Segmentation algorithm gave a lower density of false positives. It was followed by
the Unified Segmentation and finally FAST. On the other hand, Unified Segmentation
showed the lowest density of false negatives. This was followed by FAST, and finally by
New Segmentation.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
4. Study 2: Feature selection for
structural pattern recognition studies
A popular approach for analysis of structural MRI datais the concept of Voxel-Based
Morphometry (VBM) (Wright et al. 1995; Ashburner and Friston 2000). First, data are
preprocessed by classifying scans into different tissue types, which are aligned into a
common anatomical space. Following preprocessing, a statistical analysis is performed
(under some assumptions) to enable the comparison among populations. A massunivariate approach underlies the resulting maps in the SPM framework (Friston 1994).
However, variability of brain structural patterns is of a multivariate nature, so
multivariate approaches may provide a more veridical framework. Powerful machine
learning techniques from other fields have been adopted to obtain a more accurate
understanding of the different processes that occur in the brain. Having a more accurate
model may allow more rapid translation from basic research into clinical applications.
This is the role of multivariate techniques in neuroimaging (Ashburner and Klöppel 2011).
Nowadays, brain imaging researchers aim to collect the largest possible number of
subjects. Studies attempt to obtain findings that can generalize, for instance differences
between populations or the impact of a biomarker, etc. In general, these require some
form of characterization of inter-subject neuroanatomical variability. Capturing much of
the inter-subject variance among brain images involves shape modeling (computational
anatomy), where the accuracy of inter-subject registration plays a significant role in terms
of the findings and their interpretability (Ashburner and Klöppel 2011). Conclusions from
any particular study depend heavily on how the data are modeled, and the assumptions
underlying those models.
There are many different approaches to modeling such characterizations. Successful
multivariate methods do not necessarily localize differences, but instead aim to capture
the patterns of difference that best separate subjects into groups, or predict some
continuous variable of interest. Although useful for analyses that attempt to localize
differences, the widely used assumption of independence among the anatomy of different
brain regions is not really biologically plausible. If this assumption is removed, greater
predictive accuracy may be possible. For example, age or gender differences are not
localized to any particular brain region. Instead, there is a pattern of differences that are
distributed throughout the brain. Studies based on localizing differences only show the
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
most relevant aspect (like the tip of an iceberg) but they can lose important information
pertaining to patterns of relationships among brain regions. A pattern recognition
approach attempts to learn a relationship between feature data and their corresponding
labels. The algorithm, after learning such a relationship, should be able to predict the label
for new data cases.
Many different algorithms for pattern recognition analysis are available. For this thesis,
Gaussian processes for classification and regression have been used (Rasmussen and
Williams 2006). Gaussian Processes (GP) are kernel-based approaches, set in a Bayesian
framework. They achieve similar performance to Support Vector Machines (SVM) for
neuroimaging data (Schrouff et al. 2013) with the advantage that they make probabilistic
predictions. These supervised algorithms learn the mapping between the input (data
features) and its output (labels) from a set of training data. Depending on whether the
output is continuous or discrete, it would be respectively a classification or a regression
problem.
4.1 Motivation & Objectives
The motivation for this work is to determine an effective feature representation of image
data from multiple subjects, such that pattern recognition methods may be made more
accurate. This involves applying GP machine learning approaches to a number of sets of
features, derived from the same subjects’ scans, in order to predict the ages and genders of
the subjects. The hope is that this should allow an effective feature representation to be
selected, prior to further work using data from different populations of subjects. When
machine learning is applied to relatively small datasets from patient populations, it is
important to determine how best to do this beforehand. It would not be good science to
try out lots of methods, and selectively report only those that worked the best. This would
be an ineffective use of valuable data.
The objective of this study is (1) to find, if possible, the types of feature derived from T1weighted MR images that are more effective, irrespective of the target for regression and
classification. The second objective is (2) to find a good range of spatial smoothing to work
with.
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4.2 Material & Methods
A relatively large public data set with respective demographic variables was used in this
work. Several sets of features were obtained from it, using a VBM-type pre-processing.
With them, different analyses were carried out to explore the performance dependency on
the features: A GP regression (implemented as a Bayesian ridge regression analysis) to
predict age and body mass index (BMI), and a GPclassification analysis to predict gender.
4.2.1 Dataset
The IXI data set, provided by the Biomedical Image Analysis Group3, consists of a variety of
MR images from nearly 600 normal, healthy subjects with their respective demographic
information. Only the T1-weighted images were used. MRI data were acquired in three
different scanners, two of which were 1.5T and one was 3T. Table 3.1 summarises the
demographics of the sample. Subjects whose variables were not available were not
included in the analyses. Some “data scrubbing” was performed by identifying variables
which were obviously incorrect, and also excluding these from the analysis.
Table 4.1 - demographics of the sample.
4.2.2 Preprocessing
The T1-weighted images were visually inspected for possible artifacts, and approximately
aligned with the SPM template data (via translations). Next, a VBM-type pre-processing
was conducted. The default segmentation tool implemented in SPM12 was used for
segmenting the images. The SPM12 implementation is an updated version of “New
Segment” used in the Study 1. It is based on the algorithm presented in (Ashburner and
Friston 2005), but makes use of additional tissue classes, allows multi-channel
segmentation (of i.e.T2 and PD-weighted images), and incorporates a more flexible image
registration. Changes from the SPM8 New Segment include different regularization for the
deformations, some different default settings, as well as re-introducing the re-scaling of
3
available at http://biomedic.doc.ic.ac.uk/brain-development/index.php?n=Main.Datasets
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
the tissue probability maps (which was in the old segment, but not the new). In addition,
the SPM12 tissue probability maps were re-generated using the T2-weighted and PDweighted scans from the same IXI dataset. (For a more extensive description of the
differences, see the appendix of (Malone et al. 2015).
Following tissue segmentation, inter-subject registration was performed using the
Geodesic Shooting Toolbox, also implemented in SPM12. The approach is described in
Ashburner and Friston (2011), and is superficially similar to Dartel (Ashburner 2007).
Evaluations show that this model achieves more robust solutions in situations where
larger deformations are required (Ashburner and Friston 2011).
4.2.3 Data for structural feature representation
Preprocessing outputs were used as features. Each feature representation encodes a
different kind of information about the original image data. The field of view of the feature
data covers the whole brain, and the features that have been used are listed in figure 4.1.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 4.1 - Resulting images from the pre-processing and those obtained from operations, like the log. of
the Jacobians and the Background images, BG= 1-(GM+WM). All these images were tested as features.
Smoothing
Spatial smoothing of varying degrees was applied to the raw feature images. This was
intended to reduce noise and finer grain anatomical variability. Exploring the optimal
degree of smoothing is a relevant factor. If there is too much blurring, the image may lose
relevant information. On the other hand, if there is not enough blurring, differences may
be not be detected. The effect of smoothing was explored in order to find the optimal
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
amount of smoothing for each feature type. For this purpose, all data were filtered using a
range of smoothing from 0mm to 20mm FWHM. The 10 feature representations were
smoothed using the 21 measures of smoothing. The 210 sets were separately studied as
inputs in the pattern recognition approach.
Kernel matrices
In the Gaussian processes representation, from the viewpoint of linear regression, feature
data are introduced into the model in the form described in equation (1.23), becoming the
covariance function, or kernel function.
An image can be thought of as a vector in a very high-dimensional space (Fig. 4.2 (left)). If
a brain image would have only three voxels, it could be visualized as a point in a 3D space.
In practice though, the number of dimensions needed to represent a real image in this way
makes it impossible to visualize. For binary classification problems, it is possible to define
a hyper-plane dividing regions of high-dimensional space, such that one class falls in one
region and the other class in the other. Class membership is then assigned to new data,
depending which side of this hyper-plane it falls. Similar principals apply to regression,
where a continuous label is predicted instead (Ashburner and Klöppel 2011).
Fig. 4.2 – Representation of a 3D image in a feature vector.
A sample can be thought as a set of N vectors each one with k components, where k is the
number of voxels (Fig. 4.2 (right)). The kernel matrix obtained by computing XXT is an N×N
matrix that encodes the similarities among the images.
Xj
Xi
Fig. 4.3 - Representation of how a kernel matrix is created from images using the dot product.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Thus, the k dimensions encoded in each image are reduced to N. When spatial smoothing
is used, this may be conceptualized as constructing a kernel matrix from XXT, where  is
a Toeplitz matrix that enacts the spatial smoothing.
In the current study, kernels were constructed from the 210 feature sets described above.
Several new kernels were also studied, which were constructed by summing some of the
original kernel matrices together. Separately each tissue class encodes information about
itself regarding the target. The tissue class kernel matrices were combined as follows:
Table 4.2 – multi-kernels used as features.
This was done over all levels of smoothing, so 84 new kernels were added to the initial
number of 210 kernels.
Adding a variable to the model: Modulated data adjusted for Total
Intracranial Volume
In this thesis, a procedure is proposed for dealing with total intracranial volume (TIV).
Usually, when modulated data are used in a VBM analysis, TIV is either modeled as a
confounding covariate, or is used to normalize the preprocessed data by dividing regional
tissue volumes by the TIV. It is useful to include it if the aim is to observe local differences
between groups (Mechelli et al. 2005). Modulated data are corrected for regional
expansion and contraction incurred during the warping process, such that the original
regional tissue volumes are preserved. In this work, we normalise the modulated tissue
maps by dividing them by the TIV. This provides an additional set of features. For
convenience, the kernel matrices - rather than the features themselves - were normalized
(because (x1/s1)(x2/s2) = (x1x2)/(s1·s2), where s1 and s2 are TIVs). This process generated
an additional 105 kernel matrices. Results obtained from kernels that accounted for TIV
were compared to those that do not account for it, modulated and non-modulated.
The kernel matrices were used as inputs in a pattern recognition algorithm for regression
when the labels were continuous (e.g. age), and for classification when these were discrete
(gender). Gaussian process models were used to make the predictions. Specifically, the
ridge regression model described above was used for predicting age and body mass index
(BMI = weight (kg)/height (m2)). The classification model based on (Rasmussen and
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Williams 2006) was used for predicting gender. Both algorithms (GP for regression and
classification) are available as part of SPM12.
4.3 Performance evaluation
Generalization performance was assessed using a k-fold cross-validation (CV) strategy,
which allows most of the sample to be used during the training stage. The original sample
is randomly partitioned into k equal sized subsamples. One of these subsamples is
retained to be used as validation data for testing the model, and the remaining subsamples
(k-1) are used for training the model. The cross-validation process is repeated k times
(folds) with each of the k subsamples used once as test data. In those cases when k is equal
to the number of observations the k-fold CV becomes a leave-one-out cross-validation
(LOO-CV)4. This study used a 10-fold cross validation (CV), with the same subdivision into
folds for all kernel matrices.
For Regression
For regression, the model assigns a predicted value of the corresponding target. It also
provides estimates of the uncertainty in the form of standard deviations, but these were
not used. The root mean squared (RMS) error was estimated for each model (i = {age,
BMI}, features k= {GM, WM, scalar momentum, jacobians, etc…} and smoothing s= {0, 1, …,
20}) as follows:
=
∑
(
)
(4.1)
Where mj corresponds to the real value, tj is the predicted value, and N is the number of
observations. The RMS error gives a measure of how well the model can predict the real
data, and allows a comparison to be made between feature sets. RMS error was plotted
against the degree of smoothing, for kernel matrices of all feature types.
Moreover, the log-marginal likelihood 5 was considered. Predictive results are dependent
on the values of the hyper-parameters that define the behavior of the model. The optimal
choice for these parameters may be obtained by finding values that maximize the marginal
likelihood of the model. Then, the greater the log-marginal likelihood, the better is the
model fitting (Rasmussen and Williams 2006). Log-marginal likelihoods, as well as the
RMS error, are plotted in figures 4.4 and 4.6 for each feature set, over the range of
4
5
https://en.wikipedia.org/wiki/Cross-validation_(statistics)
https://en.wikipedia.org/wiki/Marginal_likelihood
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
smoothing. For the best data feature, the plot of the real target values versus the predicted
values are shown in figures 4.5 and 4.7.
For Classification
For classification, instead of obtaining a predicted variable (plus standard deviation) for
each observation, a probabilistic label of belonging to one class or another is predicted.
Due to the nature of the outcomes, other measures were considered to estimate the
performance.
The area under the curve (AUC) of the ROC curve was calculated. The ROC curve shows the
performance of the classification and is obtained using the ratio of true positives versus
the ratio of false positives as the discrimination threshold varies (threshold above which it
is said that a case is positive or not). The area under this curve is a measure of how well
the classifier has performed, being a summary of the performance of the classifier across
all decision thresholds6. When a classifier makes the perfect discrimination the AUC is 1,
when a binary classifier is guessing at chance-level, it would achieve an AUC of around 0.5.
Also, the log-marginal likelihood was computed. Log-marginal likelihood and AUC
wereplotted for all the feature datasets versus the smoothing in figure 4.8. For the best
data feature, the ROC curve is shown in figure 4.9.
Evaluation
Results obtained from using the feature datasets were plotted. For the log-marginal
likelihood and the AUC, the higherthe curve, the better the model fit. For the RMS error,
the lower the value, the better the model fit.
Plots of results from all features together would be confusing and difficult to interpret.
Therefore, depending on the origin of the data, plots have been represented by grouping
features. Results from all those features that are implicitly part of the registration process,
i.e. Jacobians, log-Jacobians, divergence of velocities, and scalar momentum, were
presented together. Results from GM, WM, BG, and combinations of these were grouped,
with results from modulated features shown separately from those without modulation.
To make comparisons easier, all the plots related to the same target measure are shown
with the same axis scale.
In order to conclude which the most efficient feature is, the optimal smooth-feature was
selected from their respective set of features according the log-marginal likelihood. RMS
6
https://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_curve
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
error for regression or the AUC for classification were also considered when assigning
rankings.
For comparing one model versus another, the Bayes Factor was used (Kass and Raftery
1995; Jeffreys 1961). Given a pair of models with the same number of hyper-parameters,
the plausibility of the two different models M1 and M2 may be (approximately) assessed
by the Bayes factor as
BF = 2·log(K) = 2·log(marginal likelihood(M1))–2·log(marginal likelihood(M2))
(4.2)
The BF value can be interpreted by means of the scale defined by Kass and Raftery (1995).
This scale varies from <0 to >10, and is divided into blocks. An increase in the BF provides
greater evidencefor one model against other.
2·log(K)
0 to 2
2 to 6
6 to 10
>10
K
1 to 3
3 to 20
20 to 150
>150
Strength of evidence
not worth more than a bare mention
positive
strong
very strong
Table 4.3 – Scale provided by Kass and Raftery for interpreting the Bayes factor7.
These representations of estimates, the log-likelihood and the RMS error/AUC, provide
complete and robust information about the performance from each feature dataset, and
allow the comparison between them from different, but complementary, perspectives.
7
https://en.wikipedia.org/wiki/Bayes_factor
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
4.4 Results
Regarding the feature datasets, in all cases the log-marginal likelihood and the RMS
error/AUC are in broad agreement with respect to the scores. An interesting aspect,
mainly related to the RMS error and the AUC, is that the curves were smooth and the best
scores covered several mm of smoothing (Figures 4.4, 4.6 and 4.8).
4.4.1 GP Regression
Age
Interestingly, the best performance was obtained from the scalar momentum, which
provided the most efficient feature at 11mm of FWHM. This was closely followed by three
different combinations of kernels from tissue types that provided good features for
predicting age. Results from the four best scores are summarized in table 3.3.
Table 4.4 – Best scores in age regression. The average age of all subjects is 46.83 years, and standard deviation
is ± 16.41 year The RMS error is markedly below this.
Remarkably, the RMS error is far below the standard deviation associated with guessing
that all subjects are of average age, which is considerably greater (±16.41 years).
Log-marginal likelihood (on the left side) and the corresponding RMS error (on the right)
associated with the same measurements are plotted in figure 4.4. When marginal
likelihoods from best features are compared by means of the Bayes factor, differences
between models are greater than 2 in all cases. Comparison between scalar momenta with
the second in the ranking is 3.2 according the Kass and Raftery’s scale, indicating that
differences are positive. Difference estimated with respect to the GM+WM achieved 8
points in the scale, indicating strong evidence that scalar momenta outperformed this
combination of kernels.
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Fig 4.4 -AGE: (a) Scalar momenta, Jacobians, log-Jacobians and divergence of velocities.(b) GM, WM, BG and
combinations:GM+WM and GM+WM and GM+WM+BG. (c) Scaled GM, WM, BG and combinations of scaled
GM+WM and scaled GM+WM+BG.(d) Scaled data adjusted for TIV.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
When plots are observed, it is noticeable that differences in log-marginal likelihood for
each feature markedly varied with the smoothing. Bayes factor differences overtook the
strong evidence from 0 to 20 in most of the cases. With smoothing, the feature from scalar
momentum outperformed the rest and good results were generally obtained from kernel
matrices created from the sum of kernel matrices from GM, WM and BG.
Without any smoothing, the logarithms of the Jacobians provided very effective features. A
surprising result was that modulated GM was not a very effective feature for making age
predictions.
A combination of kernel matrices from GM, WM and BG modulated provided better
performance when accounting for TIV than those without TIV. The Bayes factor gave very
strong evidence for this.
GM encoded more information about age than WM or BG, although its performance was
not as good as expected. Interestingly, combining kernel matrices from GM, WM and BG
provided better age predictions than using any of these kernel matrices alone.
The best performing feature set for predicting age was the scalar momentum. Figure 4.5
shows real ages plotted against predicted ages, and the best fit through this plot.
Fig. 4.5- Real versus predicted ages and linear fitting associated to the most effective feature.
BMI
Results showed that WM was a relatively effective feature for predicting BMI. In addition,
the combination of the WM with GM and BG reached high scores. The scalar momenta are
also in the ranking as one of the best features that better encoded the BMI pattern (Table
4.5). It is worth noting that the RMS error (3.4kg/m2) associated with the predictions had
a similar order of magnitude to the standard deviation, ±3.8kg/m2.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Table 4.5– Best scores in BMI regression. Average and standard deviation of BMI was 24.9±3.8 kg/m2. RMS error
is much lower than the standard deviation.
Plots of log-marginal likelihood (on the left) and the corresponding RMS error (on the
right) are shown in figure 4.6.
Modulated data (with and without TIV), Jacobians and divergence of velocities did not
provide good features for predicting BMI.
With smoothing, scalar momenta gave similar results to WM. From about 10mm of FWHM,
scalar momentum seemed to be a good feature for predicting BMI. However, in
comparison to the WM, there was strong evidence according the Bayes factor that WM was
a better model than scalar momentum. Same occurred with the combination of GM and
WM. Regarding the sum of tissues GM, WM and BG, the Kass Raftery scale stated that there
was very strong evidence that WM was a better model.
Performance of WM remarkably increased with the smoothing and provided very effective
feature for predicting BMI. Regarding the kernels from combining WM with GM and with
GM+BG, their performance showed very strong evidence of being poorer models than only
using WM, according to the Kass and Raftery scale for the Bayes Factor. Contribution of
GM and BG tissues to WM were noisier than using only WM for predicting BMI.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig 4.6 – BMI: (a) Scalar momenta, Jacobians, log-Jacobians and divergence of velocities. (b) GM, WM, BG and
combinations: GM+WM and GM+WM and GM+WM+BG. (c) Scaled GM, WM, BG and combinations of scaled
GM+WM and scaled GM+WM+BG. (d) Scaled data adjusted for TIV.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Combinations aside, WM and scalar momenta werefeatures that better predicted BMI.
Figure 4.7 shows plots of real BMI with respect to predicted BMI, and the linear regression
fit for both features.
Fig. 4.7–WM and scalar momentum provided best feature representations for predicting BMI.
4.4.2 GP Classification
Gender
Scalar momentum was the best feature for predicting gender. Also, all the possible
combinations of GM, WM and BG exhibited high performance. Results are detailed in Table
4.6.
Table 4.6 – Best scores in Gender classification.
From the listed features, good scores in performance covered a wide range of smoothing
degrees. The AUC reached 0.971 at 6mm of FWHM and slightly varied to reach the
maximum at 15mm, 0.975. The scalar momenta achieved higher performance from 10mm
smoothing upwards. Plots of log-marginal likelihood (on the left) and the corresponding
AUC (on the right) are shown in figure 4.8.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig 4.8 –GENDER: (a) Scalar momenta, Jacobians, log-Jacobians and divergence of velocities. (b) GM, WM, BG and
combinations: GM+WM and GM+WM and GM+WM+BG. (c) Scaled GM, WM, BG and combinations of scaled
GM+WM and scaled GM+WM+BG. (d) Scaled data adjustedfor TIV.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
WM was the worst feature for predicting gender, whereas BG and GM appeared
competitive with the combination of GM, WM and BG.
With smoothing, all tissues and their combinations were better features. The sum of
kernel matrices constructed from the three tissue types, with and without modulation,
were very effective features for classifying gender.
On the other hand, Jacobians and divergence of velocities were good features. Better
scores were reached at lower FWHM sizes, although the dependence of performance on
the smoothing was relatively low.
Scalar momentum was the feature that best predicted gender. The ROC curve shows the
performance of the classification at 10mm of FWHM, with an AUC of 0.98.
Fig 4.9 – ROC curve and AUC associated to the prediction of gender
from scalar momentum at 10mm of FWHM.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
5. Study 3: Application to Schizophrenia
One of the main purposes of the current thesis is the application of improved
methodologies for clinical research. Finding specific morphometric alterations associated
with a particular disease is a widespread goal in neuroimaging research. It has been done
in hundreds of studies, mainly from applying Voxel-Based Morphometry (VBM)
(Ashburner 2009). Mass-univariate approaches, such as VBM, allow volumetric differences
in tissue classes among populations to be localized. However, these methods assume that
voxels are independent, which may not be the most biologically plausible assumption to
make. A number of works have identified significant amounts of covariance among tissue
volumes in different brain regions (Westman et al. 2011; Modinos et al. 2012). Recent
developments involve using a multivariate analysis framework, such as pattern
recognition approaches. These often provide greater accuracy for characterizing
differences between populations of subjects (Schrouff et al. 2013). As shown in study 2,
these approaches generally involve pre-processing anatomical MRI scans in the same way
as for a conventional VBM study, but then applying a pattern recognition analysis.
In this study, some methodological aspects regarding pattern recognition and features
from MRI data, which were previously explored in study 2, have been applied to
Schizophrenia.
Chronic Schizophrenia is a widely studied disease that is still an object of study, and
provides a clinically useful setting for applying methodological aspects that have been
explored in previous chapters. Nowadays, there are consistent findings that have allowed
the characterization of the anatomical pattern associated with this disease. Schizophrenia
is characterized by a reduction, of around 2%, in whole brain volume. Locally, larger
reductions in regions such as the frontal lobe, in about 50% of VBM studies, and
hippocampus, insula, temporal and parietal cortices, in about 20%, are reported (Honea et
al. 2005). Other regions are also strongly involved in the disease, such as the medial
frontal cortex (Bora et al. 2011), which has been proposed as a key region. Ellison-Wright
and Bullmore (Ellison-Wright and Bullmore 2010) performed a meta-analysis of 42 VBM
studies of schizophrenia, where they found that the distribution of GM volume reductions
was wider in schizophrenia than for other mental diseases, such as bipolar disorder,
affecting frontal, temporal, cingulate, insula and thalamus. Postmortem studies support all
these findings (Brown et al. 1986; Pakkenberg 1987; Bogerts et al.). All this information
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
leads to a conclusion that GM is a tissue highly involved in the disease, and that the pattern
of brain damage may be more global than neuroimaging findings so far suggest.
5.1 Motivation & Objectives
The current work consists in applying GP classification to Schizophrenia using:
(i)
GM tissue class, which encodes key information about the disease, and
(ii) Scalar momentum, which was found in study 2 to be a very efficient feature for
predicting structural patterns of differences.
Subsequent performance results from the different feature sets were compared.
The objective is (1) to assess whether scalar momentum provides a good feature, (2) to
test whether GM is really one of the best data features for predicting schizophrenia, and
(3) to determine the optimal degree smoothing to apply to image data in order to predict
schizophrenia.
5.2 Material & Methods
In this Study, anatomical MRI data from patients with schizophrenia and healthy subjects
were pre-processed. A conventional VBM analysis was carried out to see GM volume
differences associated with the sample. Next, the same sample was used for predicting
disease using GP classification. Two different data features were used: GM and scalar
momentum. For exploring the behavior regarding the degree of smoothing, several sizes of
FHWM were used.
5.2.1 Participants
The sample of 111 patients with schizophrenia was recruited from Benito Menni CASM
(40.94±8.75 years old; 33women), and the 111 healthy subjects came from a database of
controls recruited from hospital staff and their acquaintances (40.14±10.11 years old; 33
women).
All participants were right-handed Spanish Caucasian. Pre-morbid IQ was estimated using
the Word Accentuation Test (Del Ser et al. 1997; Gomar et al. 2011), which involves
pronunciation of words whose accents are removed (score for healthy subjects:
23.07±4.54 and patients: 20.22±5.56).
Patients met DSM-IV criteria for schizophrenia, based on interviews by two psychiatrists
and a review of case-notes, and were required to have a current IQ in the normal range
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(i.e. 70+), as measured using four subtests of the Wechsler Adult Intelligence Scale III
(WAIS-III) (vocabulary, similarities, block design, and matrix reasoning). All were scanned
when in a relatively stable condition and all were taking antipsychotic medication.
Patients were included if they (a) were between18 and 65 years old, (b) had no history of
brain trauma or neurological disease, and (c) had not shown alcohol/substance abuse
within the 12 months prior to participation. Controls met the same criteria as the patients,
and were questioned and excluded if they reported a history of mental illness and/or
treatment with psychotropic medication.
Participants gave written informed consent, and the study was approved by the local
hospital ethics committee. These data have been used previously in other studies
(Pomarol-Clotet, Fatjó-Vilas, et al. 2010; Sans-Sansa et al. 2013; Sarró et al. 2013).
All subjects underwent structural MRI scanning using the same 1.5 T GE Signa scanner
(General Electric Medical Systems, Milwaukee, WI, USA), located at the Sant Joan de
DeuHospital in Barcelona (Spain). High-resolution structural T1-weighted MRI data were
acquired with the following acquisition parameters: matrix size 512×512; 180 contiguous
axial slices; voxel resolution 0.47×0.47×1 mm3; echo (TE), repetition (TR) and inversion
(TI) times were 3.93 ms, 2000 ms and 710 ms, respectively; flip angle 15°.
5.2.2 MRI preprocessing
After visual inspection for artifacts and anatomical anomalies, datapre-processing was
carried out. The same procedure as in Study 2 was conducted using the SPM12 software
(http://www.fil.ion.ucl.ac.uk/spm; The FIL methods group; London. UK).
Images were segmented into grey matter (GM), white matter (WM), and cerebrospinal
fluid (CSF) using the “Segmentation” tool. For registration, the Geodesic Shooting Toolbox
was used (Ashburner and Friston 2011).
VBM
For the VBM analysis, warped GM tissue classes were scaled by the Jacobian. The
modulated data were smoothed by 10 mm FWHM.
Statistical analysis was performed by fitting a voxel-wise general linear model (GLM), with
corrections for multiple dependent comparisons using random field theory (Worsley et al.
1996; Worsley 2003) . A two-sample t-test was performed for comparing healthy subjects
against schizophrenia patients. The design involved age and gender as covariates, and TIV
as a “global”. Spatial locations of differences between groups were identified using a FWE
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
corrected statistical threshold of p<0.01. An extent threshold of k = 500 voxels was
applied.
GP classification
Warped GM tissue class and scalar momentum were used for predicting disease. The
smoothing applied was in the range of the optimal values in Study 2. For both data
features, smoothing from 10mm to 16mm FWHM were applied.
Predictions of the diagnostic group were carried out using the same GP classifier as in
study 2 (available within the SPM12 software). The feature datasets were used as inputs,
and transformed into linear kernel matrices using the dot product to become the
corresponding covariance functions.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
5.3 Results
5.3.1 VBM
VBM analysis detected most of the reported areas in the literature associated with
schizophrenia (Honea et al. 2005). Only one bilaterally distributed cluster was found
(Figure 5.1). It appeared symmetric and was centered at the left rectus [k= 148961,
pFWE<0.000, T= 9.84, (0, 39, -15)]. The cluster included two main peaks at the left anterior
cingulate [pFWE<0.000, T= 9.77, (2, 48, 14)] and the right cingulum middial [pFWE<0.000, T=
9.11, (9, 39, 34)]. Locations are detailed in Table 5.1.
Table 5.1 – Locations that were involved in cluster 1.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig. 5.1 – Statistical parametric map of the pattern of differences from a VBM comparison between
healthy subjects and schizophrenia patients, corrected FWE p<0.01.
5.3.2 GP classification
Scalar momentum and GM provided very effective features. However, regarding the logmarginal likelihood, scalar momentum achieved the best performance, with a smoothing
of 12mm FWHM. The corresponding AUC was 0.89. GM also was a good feature, and
performance reached same AUC as scalar momentum. The best log-marginal likelihood
score for GM was found at 11mm FWHM. However, the model fit was poorer than for the
scalar momentum. Results from all the observations are detailed in Table 5.2.
Table 5.2 – Marginal likelihood and AUC of the classification from GM and scalar momentum using a
range of smoothing comprised between 10 and 16 mm of FWHM.
Estimation of the Bayes Factor concluded that there was strong evidence that scalar
momentum provided a better model, scale strength of evidence was 7 according the Kass
and Raftery (Kass and Raftery 1995).
Plots of the log-marginal likelihood and the AUC from all the performances conducted
using GM and scalar momentum are shown in figure 5.2.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
Fig 5.2 – Performance of the predictions about disease status. Controls versus Schizophrenia: (left)
log-marginal likelihood and (right) Area under thecurve (AUC) obtained from each classification
process. Estimations were performed using scalar momenta (black) and GM (blue) using different
degrees of smoothing.
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
6. Discussion
The effect of the preprocessing steps is a sensitive issue in the classification and
regression output. It is a wide field of exploration; few works have focussed on this aspect,
in particular regarding fMRI data (LaConte et al. 2003). This thesis has contributed in this
direction, by first exploring the reliability of GM segmentation and as well as studying
different feature representations from MRI data. Also, a contribution about how TIV can be
introduced successfully into the kernel has been presented. Results have shown that scalar
momentum has become an excellent feature that allows characterising schizophrenia
better than GM.
Before registration, it was necessary to find reliable tissue classes. For this purpose, in the
study 1 three of the most frequently used segmentation pipelines, from the SPM and FSL
software packages, were compared. The challenge in tissue segmentation lies in having a
robust approach. Theoretical approaches have been presented in parallel to detect
differences and similarities and outcomes from segmentations at each step have been
empirically explored.
Some previous works compared segmentation algorithms. In Tsang et. al. (Tsang et al.
2008) they compare the same software as in the current thesis, although they used a
slightly older SPM release (SPM5), and they used the same dataset. Although there were
differences in methodology, other aspects were similar. The general conclusion was that
SPM5 gave better specificity and sensitivitythan FSL. Fellhauer et al. (Fellhauer et al. 2015)
compared SPM, FSL and FreeSurfer8. As expected, the best performances were obtained
with good quality images. With especially noisy data, the best segmentation results were
obtained using the algorithms in SPM8 and SPM12.
These results are in agreement with what was found in the current work. A relevant
remark to bear in mind is that all these works, and many others, use different
methodologies for testing segmentations. In this work, an additional contribution is that
the methodology involves new approaches for exploring data, even though strategies, the
dataset and commonly used tools (i.e. Jaccard index) are similar. On the other hand, the
8
freesurfer.net
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
methodology also stops at each step, in native and normalized spaces, and explores how
manual reorientation and skull stripping affects the segmentation process.
From preliminary evaluations, we found that manual positioning was necessary in SPM
prior to running the “Unified Segmentation”, which is in agreement with findings from
Tsang et al. (2008). In the “New Segmentation” procedure it is also necessary. Although
the estimated deformations are not extremely badly behaved, they may not be quite
accurate enough. The issue lies in the initial affine registration; therefore, positioning in
the anterior commissure is necessary to avoid the chance that the algorithm finds a local
optimum. Concerning BET, special attention must be focused on the outputs before
running the next step. A recommended option is fslvbm_1_bet with the –N command; this
works successfully and overcomes a wide range of downsides; however, it does not
guarantee that stripping will be accurate in 100% of the cases. If the stripping is not
accurate, other more restrictive options are recommended.
In the main body of the study, where false-positive and -negative images were counted,
FAST was the software with the highest amount of false negatives, and differences with
respect to NS, and also to US, were statistically significant. Regarding false positives, US
was the algorithm with highest number of them, statistically significant differences were
found with FAST and also with NS.
On the other hand, FAST tended to be more specific with respect to the other algorithms,
and US was found more sensitive than the rest. Interestingly, NS was the algorithm that
seemed more balanced regarding those aspects, it is not statistically significant with
respect to US' sensitivity, and regarding specificity, differences are not significant with
respect to FAST. Moreover, NS obtained the highest Jaccard index, and the last in the
ranking was FAST. The results indicate that NS is the most reliable of the three
segmentation algorithms. In summary, findings point to NS being the most balanced of
these three algorithms. Hence that for the study 2, the New Segmentation approach was
applied.
There are some limitations in study 1. First, at the time of the evaluations, the versions
used were the most recent. However, this is not a static field, and software versions are
updated regularly. For study 2, a more recent version of the “New Segmentation”
algorithm was used (from SPM12) compared to study 1 (SPM8). The NS method used in
study 2 involved some improvements with respect to the older version. In fact, the
modifications addressed some of the issues mentioned in this chapter.
Another limitation is related to the IBSR dataset: only one was used, and the images
contained noise and artifacts such that the dataset became a challenge for the algorithms.
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Additionally, the ground truth segmentations of GM available in the IBSR may bias the
results, this is because sulcal CSF is segmented as GM. It involves that many voxels that
were distributed all around the GM images as false negatives, are definitely wrong labeled.
Because these certainly belong to the sulcal CSF and not to the GM. The inclusion of this
voxels in the accuracy measurements definitely bias the results, this is reported and
quantified by Valverde et al. (Valverde et al. 2014). NS and US were compared among
other 10 brain tissue segmentation methods that also included FAST. Also the IBSR dataset
was used for the comparison. They concluded that SPM offers the methods that appeared
more suitable for GM tissue segmenation than the other. Remarkably, their findings were
in concordance with ours, and stated that the ground truth segmentation may bias the
performance by the algorithms (Valverde et al. 2014).
Regarding study 2, the GP machine learning approach has been used to explore different
features from structural MRI data. Many features from structural data have been studied
in this thesis. This study looked at the effectiveness of a range of features derived from
structural data. T1-weighted images were preprocessed in a VBM style, “New
Segmentation” and the “Geodesic shooting toolbox” (Ashburner and Friston 2011) of
SPM12 were used. Different outcomes from these preprocessing procedures were used as
features for predicting age, gender and body mass index (BMI). A wide range of images
involved in the transformation, like Jacobians, the logarithm of Jacobians, the divergence
of velocities and scalar momenta were explored. Also, more commonly used data, such as
spatially normalized tissue classes, with and without Jacobian scaling (“modulation”),
were evaluated. Pattern recognition evaluations were performed independently for each
kernel at each degree of smoothing. For completeness, Gaussian smoothing from 0 to 20
mm FWHM was applied to the feature data to assess its effects on predictive accuracy.
The main conclusion was that scalar momentum provided an effective and robust feature,
irrespective of the target of prediction, whether it was age, gender or BMI. In all cases, this
feature obtained a performance very similar to the tissue that biologically encoded more
information about the object of study. Best accuracies are generally assumed to be
achieved when using the tissue that is more closely related to the biological process.
Findings are in agreement with a previous work by Marquand et al. (Marquand et al.
2013) where they showed that the scalar momentum are a good feature for improving
classification performance usign structural MRI data.
Allometry between brain and body allows empirical scaling factors to be recognized. An
interesting example of this was white matter (WM) for predicting BMI, which was found to
provide the best feature. Previous findings in the literature have indeed established that
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Computational analysis of Schizophrenia: Implementation of a multivariate model of anatomical differences
there is a relationship between BMI and WM (Segura and Jurado Luque 2009; Seitz et al.
2015; Ou et al. 2015).
However, information about what tissue is likely to encode much of some biological
process is generally not known a priori. In those cases, scalar momentum can be presented
as the best option to start with. This is valuable for several reasons: First for obtaining a
competitive predictive performance; second, scalar momentum can be used as a strategy
to find the tissue that encodes more of the underlying biological information.
Performance from scalar momentum was not highly dependent on the degree of
smoothing, achieving good scores from about 4 mm up to 20 mm FWHM, although the best
behavior was from smoothness above 10 mm. However, the optimal smoothing may
depend on the number of training images. For this thesis, a sample of 562 subjects was
used, but less smoothing would probably be needed with more data. Interestingly, without
any smoothing, the logarithm of Jacobians seemed to be the most useful of all features.
One surprising result was that modulated GM was not a very effective feature for making
age predictions. Brain ageing has been found to follow a specific pattern in which GM
volume plays a relevant role with respect the other tissues. It was found that GM increases
from birth until the age of four and then decreases until the 70s (Pfefferbaum et al. 1994).
More recent studies have found that GM decreases linearly with age, while WM did not
(Good et al. 2001). These, among other studies, justify that GM were used as feature in a
number of studies, but the current work suggests that the results of those studies could
have been improved. Information from Jacobian-scaled GM only became effective when
combined with Jacobian-scaled information from the rest of the image.
Another aspect in this study that is worth mentioning is that TIV was introduced in the
prediction model. Kernels from modulated data were divided by the product of TIV
associated to each pair of subjects. Such an operation should be equivalent to dividing
each subject image for TIV, however, in this way calculations were extremely simplified.
Results suggested that accounting for TIV increased the performance from modulated
data. This fact makes sense, like in VBM analyses (Mechelli et al. 2005), because the data
account for real differences in volume and not for contractions and expansions due to
registration transformations to the standard space.
A limitation of this study could be the size of the sample; 562 subjects is not a small
number of inputs, but for pattern recognition studies, a larger number of samples is
desirable. The behavior of the smoothing would vary with a larger number of subjects, so
possibly a lower amount of blurring is required.
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In the study 3, a VBM analysis was performed and the results confirmed that grey matter
(GM) is strongly involved in schizophrenia. The same pattern of damage as reported in the
literature was found. These findings confirmed that GM contains a large amount of
information about schizophrenia. After that, scalar momentum was used as feature for
predicting schizophrenia, and the performance was compared to that obtained from using
GM. A range of smoothing of between 10 mm and 16 mm full-width-at-half-maximum
(FWHM) was considered.
The classification of schizophrenia using MRI has been studied extensively, and several
papers using a variety of pattern recognition approaches have appeared. In most of them
Support Vector Machines (SVM) were used; in some cases, structural GM data were used
to study first-episode schizophrenia (Pina-Camacho et al. 2015; Mourao-Miranda et al.
2012), and schizophrenia in general (Nieuwenhuis et al. 2012), with respect to data of
relatives. Sometimes this also involved using white matter (WM) as a feature (Fan et al.
2008). Regarding the machine learning approach, Support Vector Machines (SVM) are
generally used more widely than Gaussian Processes (GP), although GP have been applied
with GM structural data to other diseases, such as Alzheimer’s disease (Young et al. 2012).
Only in few cases where MRI data were used, the involved features were not GM or WM.
For instance, Jacobians were used with SVM for characterizing a schizophrenia pattern
(Yushkevich et al. 2005). However, using scalar momentum instead of GM or any other
tissue class is not wide-spread practice.
This study contributes not only by showing that GP achieve a similar performance to SVM
for neuroimaging data (Schrouff et al. 2013; Challis et al. 2015), but also shows that GP
models make probabilistic predictions. Moreover, scalar momentum provides an excellent
feature for pattern recognition studies, which is highly relevant. This work shows that this
feature is competitive with the single tissue that encodes most about the biological
process being studied, sometimes achieving better performance than expected from the
best single tissue type.
GM has been widely proposed to be the best candidate to explain differences between
schizophrenia patients and healthy subjects. In this study, this tissue was found to be a
good feature for predicting schizophrenia, giving as expected a competitive performance.
In fact, the AUC of GM and scalar momentum was 0.89. However, the Bayes Factor (Kass
and Raftery 1995) provided strong evidence that the scalar momentum could be a better
feature than GM. These results were in agreement with what was hypothesized from the
conclusions in study 2.
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On the other hand, the smoothing degree that initially was supposed to be the best for GM
(~15mm), was finally centered around 11mm FWHM, which was lower than expected. For
scalar momentum, a kernel of 12 mm FWHM was applied, which was within in the
expected range.
The aim of this work is not clinical; rather, the aim is to explore whether scalar momentum
provides a feature that performs well, irrespective of the target when using real clinical
data. The outcome of this exploration suggests that Gaussian processes and scalar
momentum can contribute to clinical research on mental and neurodegenerative diseases.
This line of work could aid routine clinical practice in delimiting differential diagnoses,
and in reinforcing clinical treatments, which sometimes are not clear.
A limitation of this work is the size of the sample, which is smaller than in study 2; the
current classification involved 222 subjects. Further analyses should be performed with
larger samples of healthy subjects and patients. Several interesting designs could be
explored to study the scope of using scalar momentum in depth, for instance by
attempting to discriminate between two different diseases that share some common
aspectsinstance. Examples of these could be schizophrenia, bipolar, and schizoaffective
disorders. This approach should be tested in neurodegenerative diseases, like Alzheimer’s
disease (AD), and also Pre-clinical and Prodromic AD.
In this study, scalar momentum provided a very efficient feature for predicting
schizophrenia, and improved the performance obtained by using GM. Initially, the tissue
class was considered the most relevant feature and the fact that scalar momentum
outperformed the results from GM confirms that scalar momentum encodes relevant
information about the biological course of the disease.
In summary, the aim of study 2 was to explore and optimize a multivariate model of
anatomical differences, and to apply the observations to schizophrenia in the next study.
In study 3, scalar momentum provided very efficient feature; the feature achieved better
than GM, which was initially the best candidate to explain differences between
schizophrenia patients and healthy subjects. The most relevant aspect from these studies
relies on this particular feature that outperformed the rest independently of the target.
The main result of this thesis was that scalar momentum provided very efficient and
robust feature in all cases. This feature achieved a performance that was very similar, and
even better than the tissue that biologically encoded more information about the target.
Interestingly, BMI was predicted succesfully using WM; scalar momentum provided a very
competitive performance with this tissue class. However, WM outperformed all the
features used. On the contrary and against expectations, GM was not the feature that
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better predicted age. Scalar momentum provided the best feature to predict age, and GM
was not among the best features.
Scalar momenta were obtained using the Geodesic Shooting Toolbox (Ashburner and
Friston 2011), implemented in SPM12. This is a tool for modeling shapes of the brain,
based on the diffeomorphic framework (M. Miller et al. 1997; Grenander and Miller 1998;
M. I. Miller 2004). The preprocessing provides a potentially more accurate shape model. In
particular, scalar momentum seemed to encode relevant information about brain anatomy
and can be interpreted as the ensemble of the warped tissue types involved in the
preprocessing, i.e. GM, WM and BG, even though scalar momentum has no straightforward
biological interpretation (Ashburner and Klöppel 2011).
A variety of spatial normalization approaches, along with their settings, could have been
explored in order to assess which gave more effective feature representations. Previous
work by Klein et al. (2009) compared a number of widely used nonlinear registration
algorithms, and found that Dartel (Ashburner 2007) was one of the more accurate
registration tools. This paper did not assess the Geodesic Shooting toolbox (Ashburner and
Friston 2011) of SPM12, which was released later. More recent evaluations (Ashburner
and Friston 2011), using some of the same data as those of the Klein et al. paper (Klein et
al. 2009), have shown that Geodesic Shooting slightly outperforms Dartel.
6.1 Outlook
Further works might be conducted based on the current work. Regarding segmentation,
new versions of the algorithms should be explored; it is desirable that all aspects that
arose from the comparisons would be addressed in future work. Other work arises from
the way the TIV was added to the kernel; this application could be used with other
variables, for instance to include them as nuisance variables in the model. Also,
considering the surprising effectiveness of the scalar momentum, studying registration,
the model and its outcomes in depth, could become an interesting line of work. Finally,
considering the scope of the findings, the presented methodology may be evaluated in
other psychiatric and also neurodegenerative diseases. Pattern recognition techniques
may strongly contribute to neuroscience, and more importantly could be used in clinical
practice for an improvement of those aspects that still remain controversial.
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7. Conclusions
In order to answer the issues that initially were posed, three different studies have been
designed. Throughout these works, the most relevant steps that may interfere with the
process to accomplish the main objective were identified and explored; eventually, we
obtained the following conclusions:
1. A comparison between segmentation pipelines, -FAST from FSL, US and NS from SPM-,
was performed. NS was found to be the most balanced algorithm regarding the number of
false-positives and -negatives and the reliability of the GM class w.r.t. the gold standard.
Manual reorientation was confirmed to be necessary in SPM, although it became less
relevant in NS than in US. Regarding FAST, the optimal command to perform skull
stripping was fslvbm_1_bet –N, although this was not accurate when facing some
particularly problematic images.
2. The GP machine learning approach was used to test different features from structural
MRI data. VBM-type preprocessing was conducted and outputs were used as features.
Scalar momentum was found to be one of the most effective features for predicting age,
gender and BMI. Against expectations, Jacobian scaled GM was not found to be a
particularly good feature for predicting age. Interestingly, WM proved to be very effective
for predicting BMI.
3.
The performance of the predictions was highly dependent on the smoothing.
Jacobians and divergence of velocities provided better features with absent or lower
smoothing. Tissue classes, modulated and non-modulated, gave better performances with
a higher amount of smoothing. Positively, scalar momentum did not play a strongly
subordinate role to the smoothing.
4.
The novel strategy - introducing TIV into the kernels for GP prediction from
modulated tissues - resulted in a better performance than using the same kernels without
accounting for TIV.
5.
Scalar momentum with 12mm FWHM of smoothing obtained the best log-marginal
likelihood fit when classifying controls and schizophrenia patients. The Bayes Factor
provided strong evidence that scalar momentum is a better feature than GM, even though
both features achieved the same AUC (0.89).
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6.
The final conclusion from this thesis is that multivariate pattern recognition analyses
using scalar momentum as feature provide an excellent strategy for classifying
schizophrenia. This approach might potentially be extended to other psychiatric and
neurodegenerative diseases, both in research and as an aid to differential diagnosis in
routine clinical practice.
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